Frank Harary

Q: What Schools Are Affiliated With Frank Harary

Frank Harary is affiliated with the following schools: University of California, Berkeley, University of Michigan, Princeton University, Brooklyn College, New Mexico State University, New York University

Frank Harary's AcademicInfluence.com Rankings

Frank Harary

Mathematics

#122

World Rank

#306

Historical Rank

#50

USA Rank

Graph Theory

World Rank

Historical Rank

USA Rank

Measure Theory

World Rank

#25

Historical Rank

USA Rank

mathematics Degrees

Download Badge

Mathematics

Frank Harary's Degrees

Bachelors Mathematics Brooklyn College

Similar Degrees You Can Earn

Best Online Bachelor's in Math Ranked

Why Is Frank Harary Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Frank Harary was an American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs. He broadened the reach of this field to include physics, psychology, sociology, and even anthropology. Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games—for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle . Because of the theorem on friends and strangers, one team or the other would have to win.

(See a Problem?)

Frank Harary's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Graph theory (1969) (17745)
Structural balance: a generalization of Heider's theory. (1956) (2193)
Distance in graphs (1990) (1358)
On the notion of balance of a signed graph. (1953) (933)
Graphical enumeration (1973) (685)
Eccentricity and centrality in networks (1995) (407)
On the corona of two graphs (1970) (406)
A survey of the theory of hypercube graphs (1988) (364)
On Eulerian and Hamiltonian Graphs and Line Graphs (1965) (337)
New directions in the theory of graphs (1973) (332)
THE MAXIMUM CONNECTIVITY OF A GRAPH. (1962) (318)
The cohesiveness of blocks in social networks: Node connectivity and conditional density (2001) (308)
Planar Permutation Graphs (1967) (300)
Chemical graphs—V : Enumeration and proposed nomenclature of benzenoid cata-condensed polycyclic aromatic hydrocarbons (1968) (286)
Some properties of line digraphs (1960) (274)
Structural Models in Anthropology (1986) (267)
Conditional connectivity (1983) (258)
Status and Contrastatus (1959) (228)
Which graphs have integral spectra (1974) (222)
The Determinant of the Adjacency Matrix of a Graph (1962) (203)
A formal system for information retrieval from files (1970) (177)
What is a System (1981) (177)
Additivity of the genus of a graph (1962) (171)
Generalized Ramsey theory for graphs (1972) (170)
A Procedure for Clique Detection Using the Group Matrix (1957) (168)
COVERING AND PACKING IN GRAPHS, I. (1970) (167)
Generalized Ramsey theory for graphs. III. Small off-diagonal numbers. (1972) (164)
The Theory of Round Robin Tournaments (1966) (162)
Domination alteration sets in graphs (1983) (154)
Graph theory in network analysis (1983) (151)
Proof Techniques in Graph Theory (1970) (146)
Dynamic graph models (1997) (143)
Graph Theory As A Mathematical Model In Social Science (1953) (142)
Radio labelings of graphs (2001) (140)
On the measurement of structural balance (2007) (131)
THE NUMBER OF LINEAR, DIRECTED, ROOTED, AND CONNECTED GRAPHS (1955) (130)
On the geodetic number of a graph (2002) (129)
Covering and packing in graphs. III: Cyclic and acyclic invariants (1980) (123)
Convexity in graphs (1981) (123)
The number of caterpillars (1973) (116)
On the Number of Husimi Trees: I. (1953) (116)
An interpolation theorem for graphical homomorphisms (1967) (113)
Graphical properties of polyhexes: Perfect matching vector and forcing (1991) (113)
On double and multiple interval graphs (1979) (110)
The number of homeomorphically irreducible trees, and other species (1959) (108)
Double Domination in Graphs (2000) (107)
Properties of almost all graphs and complexes (1979) (106)
A simple algorithm to detect balance in signed graphs (1980) (106)
Generalized Ramsey theory for graphs. II. Small diagonal numbers (1972) (102)
A structural analysis of the situation in the Middle East in 1956 (1961) (101)
Cospectral Graphs and Digraphs (1971) (101)
The enumeration of tree-like polyhexes (1970) (99)
The geodetic number of a graph (1993) (96)
A Mathematical Model for Structural Role Theory, I (1962) (91)
On acyclic simplicial complexes (1968) (91)
The Dynamics of Brand Loyalty: A Markovian Approach (1962) (90)
A graph theoretic approach to matrix inversion by partitioning (1962) (87)
A Graph Theoretic Method for the Complete Reduction of a Matrix with a View Toward Finding its Eigenvalues (1959) (86)
On the computer enumeration of finite topologies (1967) (85)
On the Tree Graph of a Matroid (1972) (84)
Topics in graph theory (1979) (83)
Covering and packing in graphs IV: Linear arboricity (1981) (83)
Cluster Inference by using Transitivity Indices in Empirical Graphs (1982) (83)
On the group of the composition of two graphs (1959) (82)
Edge fault tolerance in graphs (1993) (82)
On the Number of Crossings in a Complete Graph (1963) (81)
Nordhaus-Gaddum inequalities for domination in graphs (1996) (79)
The biparticity of a graph (1977) (78)
Finite Graphs and Networks, An Introduction with Applications. (1967) (77)
Geodetic sets in graphs (2000) (74)
Trees with Hamiltonian square (1971) (74)
Graph Theoretic Methods in the Management Sciences (1959) (73)
A SEMINAR ON GRAPH THEORY (1969) (72)
Recent results on generalized Ramsey theory for graphs (1972) (72)
Every planar graph with nine points has a nonplanar complement (1962) (71)
Island Networks: Communication, Kinship, and Classification Structures in Oceania (1996) (70)
On the thickness of the complete bipartite graph (1964) (70)
Knots and Graphs I-Arc Graphs and Colorings (1999) (70)
The Dissimilarity Characteristic of Husimi Trees (1953) (70)
The Genus of the n-Cube (1965) (69)
Exchange in Oceania: A Graph Theoretic Analysis (1991) (68)
Sum graphs over all the integers (1994) (67)
The Characteristic Polyomial Does Not Uniquely Determine the Topology of a Molecule (1971) (66)
Paley graphs satisfy all first-order adjacency axioms (1981) (65)
On the Möbius Ladders (1967) (65)
Graphs as models of communication network vulnerability: Connectivity and persistence (1981) (63)
Boolean Operations on Graphs. (1967) (62)
Extremal results on the geodetic number of a graph (1988) (59)
The Thickness of the Complete Graph (1965) (58)
The Number of Plane Trees (1964) (57)
The spectral approach to determining the number of walks in a graph (1979) (57)
The connectivity function of a graph (1967) (56)
Destroying automorphisms by fixing nodes (2006) (54)
Subcube Fault-Tolerance in Hypercubes (1993) (54)
Isomorphic factorisations. I. Complete graphs (1978) (53)
On the thickness of the complete graph (1964) (53)
On the number of bi-colored graphs. (1958) (53)
Bigraphs versus digraphs via matrices (1980) (51)
Twenty-step algorithm for determining the asymptotic number of trees of various speces (1975) (51)
Uniquely colorable graphs (1969) (50)
Matrix measures for transitivity and balance (1979) (50)
The graph reconstruction number (1985) (50)
The power group enumeration theorem (1966) (50)
The square of a tree (1960) (49)
A survey of the reconstruction conjecture (1974) (49)
On local balance and $N$-balance in signed graphs. (1955) (47)
The Reconstruction of a Tree from its Maximal Subtrees (1966) (47)
On the determination of redundancies in sociometric chains (1952) (46)
ON THE DIMENSION OF A GRAPH (1965) (46)
On the cell-growth problem for arbitrary polygons (1975) (46)
The communication problem on graphs and digraphs (1974) (45)
Chapter 1 – LABELED ENUMERATION (1973) (45)
A Characterization of Block-Graphs (1963) (44)
Interpolation theorem for diameters of spanning trees (1983) (44)
Achievement and Avoidance Games for Graphs (1982) (41)
On the problem of reconstructing a tournament from subtournaments (1967) (41)
Connectedness of Products of Two Directed Graphs (1966) (40)
Identification of the Liaison Persons of an Organization Using the Structure Matrix (1955) (40)
Generalized ramsey theory for graphs, x: double stars (1979) (40)
Outerplanar Graphs and Weak Duals (1974) (39)
The Automorphism Group of a Hypercube (2000) (39)
Signed graphs for portfolio analysis in risk management (2002) (39)
Consistent graphs with signed points (1978) (38)
The Diameter of a Graph and Its Complement (1985) (38)
EVOLUTION OF THE PATH NUMBER OF A GRAPH: COVERING AND PACKING IN GRAPHS, II††This research was supported in part by a grant to the Research Center for Group Dynamics of the University of Michigan from the NIH Biomedical Sciences Division. (1972) (37)
The number of functional digraphs (1959) (37)
The crossing numbers of some generalized Petersen graphs. (1981) (37)
Enumeration of Finite Automata (1967) (37)
A Description of Strengthening and Weakening Members of a Group (1959) (36)
Isomorphic factorizations X: Unsolved problems (1985) (35)
A Dual form of Kuratowski's Theorem (1965) (35)
Matroids versus graphs (1969) (35)
On the out-domination and in-domination numbers of a digraph (1999) (34)
DETERMINANTS, PERMANENTS AND BIPARTITE GRAPHS, (1969) (34)
Independent domination in hypercubes (1993) (33)
Classification of interpolation theorems for spanning trees and other families of spanning subgraphs (1989) (33)
Ambivalence and indifference in generalizations of structural balance (1970) (33)
On the Coloring of Signed Graphs. (1968) (33)
Changing and Unchanging the Diameter of a Hypercube (1992) (32)
Regular graphs with given girth pair (1983) (32)
Generalized ramsey theory for graphs, I. Diagonal numbers (1973) (31)
A graph and its complement with specified properties. I: Connectivity. (1979) (31)
Consistency in marked digraphs. (1978) (31)
Size in maximal triangle-free graphs and minimal graphs of diameter 2 (1995) (31)
A graph theoretic approach to the investigation of system‐environment relationships† (1977) (30)
Toward a General Calculus of Phonemic Distribution (1957) (30)
The Maximum Number of Strongly Connected Subtournaments* (1965) (30)
Generalized Ramsey theory for graphs IV, the Ramsey multiplicity of a graph (1974) (29)
Node fault tolerance in graphs (1996) (29)
Is the null-graph a pointless concept? (1974) (28)
Which Nonnegative Matrices are Self-Inverse? (1976) (27)
Methods of Destroying the Symmetries of a Graph (2001) (27)
Connectivity in digraphs (1971) (27)
On the number of cycles in a graph (1971) (27)
Some Historical and Intuitive Aspects of Graph Theory (1960) (26)
On the Spectrum of a Complete Multipartite Graph (1980) (26)
On the Consistency of Precedence Matrices (1960) (25)
Which trees are link graphs? (1980) (25)
A Matrix Approach to Nonstationary Chains (1970) (24)
The cutting center theorem for trees (1971) (24)
Counting balanced signed graphs using marked graphs (1981) (24)
Hamiltonian threshold graphs (1987) (23)
On the matching properties of three fence graphs (1993) (23)
Achievement and avoidance games for generating abelian groups (1987) (23)
The number of oriented graphs. (1957) (23)
Exponentiation of Permutation Groups (1959) (23)
What is the difference between the domination and independent domination numbers of a cubic graph? (1991) (22)
Cell‐shedding transformations, equivalence relations, and similarity measures for square‐cell configurations (1997) (22)
CHAPTER 3 – BALANCE AND CLUSTERABILITY: AN OVERVIEW (1979) (22)
A matrix criterion for structural balance (1960) (22)
A simpler counterexample to the Reconstruction Conjecture for denumerable graphs (1972) (22)
Tattooing, gender and social stratification in Micro-Polynesia (1996) (22)
The number of perfect matchings in a hypercube (1988) (22)
Graphs and applications: Proceedings of the First Colorado Symposium on Graph Theory (1985) (21)
Line removal algorithms for graphs and their degree lists (1976) (21)
Isomorphic factorisations III: Complete multipartite graphs (1978) (21)
On graphs with signed inverses (1988) (21)
Logical Foundations of Kinematic Chains: Graphs, Line Graphs, and Hypergraphs (1990) (20)
Inequalities involving the genus of a graph and its thicknesses (1965) (20)
Analysis of Interconnected Decision Areas : an Algorithm for Project Development (1965) (20)
A criterion for planarity of the square of a graph (1967) (20)
Graphs and Matrices (1967) (19)
Spanning subgraphs of a hypercube iii: meshes (1988) (19)
Graphical shapes: Seeing graphs of chemical curves and molecular surfaces (1988) (19)
Abstract sphere-of-influence graphs (1993) (19)
Digital metrics: A graph-theoretical approach (1984) (18)
Graph Theory and Geography: An Interactive View (Ebook) (2002) (18)
A survey of generalized ramsey theory (1974) (18)
Similarity and complexity of the shapes of square-cell configurations (1991) (18)
On the critical lines of a graph. (1967) (18)
On the euclidean dimension of a wheel (1988) (18)
The Number of Complete Cycles in a Communication Network (1954) (18)
Extremal problems in geodetic graph theory (1998) (18)
On the genus of an n-connected graph (1964) (18)
The $k$-tuple domatic number of a graph (1998) (18)
Digraphs with real and gaussian spectra (1980) (18)
Graph theory and electric networks (1959) (17)
GEODETIC GAMES FOR GRAPHS (1985) (17)
Maximum versus minimum invariants for graphs (1983) (17)
Enumeration of Bicolourable Graphs (1963) (17)
On the corona of two graphs (1970) (17)
A Mathematical Model for Structural Role Theory, II (1964) (16)
On the order of the group of a planar map (1966) (16)
Interpolation Theorems for the Independence and Domination Numbers of Spanning Trees (1988) (16)
Enumeration of graphs with signed points and lines (1977) (16)
Balance in stochastic signed graphs (1979) (16)
Enumeration of mixed graphs (1966) (16)
On the Hall Number of a Graph (2000) (16)
A graph theoretic approach to similarity relations (1964) (15)
Cubic identity graphs and planar graphs derived from trees (1970) (15)
The starlike trees which span a hypercube (1988) (15)
The smallest graph whose group is cyclic (1966) (15)
A graph and its complement with specified properties. IV. Counting self-complementary blocks (1981) (15)
On signed degrees in signed graphs (1994) (15)
Geodetic contraction games on graphs (1989) (14)
Generalized Ramsey Theory for Graphs V. the Ramsey Number of a Digraph (1974) (14)
Two graph-colouring games (1993) (14)
A Survey of Graphical Enumeration Problems††Work supported in part by grants from the Air Force Office of Scientific Research and the National Science Foundation. (1973) (14)
Residually-Complete Graphs (1980) (14)
A Survey of Combinatorial Theory (2014) (14)
ON THE CLASS-RECONSTRUCTION NUMBER OF TREES (1988) (14)
The square of a chordal graph (1994) (13)
The smallest graphs with certain adjacency properties (1980) (13)
Wealth and Hierarchy in the Kula Ring (1986) (13)
Enumeration of Locally Restricted Digraphs (1966) (13)
Pollution Beliefs in Highland New Guinea (1981) (13)
A City is Not a Semilattice Either (1976) (13)
The number of plane trees with a given partition (1964) (13)
Isomorphic factorisations V: Directed graphs (1978) (13)
Dissimilarity characteristic theorems for graphs (1960) (12)
On minimal feedback vertex sets of a digraph (1975) (12)
Aesthetic Tree Patterns in Graph Theory (1971) (12)
Efficiency of dissemination of information in one‐way and two‐way communication networks (1974) (12)
Mediation and Power in Melanesia (1981) (12)
The structure of threshold graphs (1979) (12)
Mathematical aspects of electrical network analysis (1971) (12)
On signed digraphs with all cycles negative (1985) (12)
Chiral and achiral square-cell configurations; the degree of chirality (1991) (11)
MEASUREMENT OF THE INTERACTIVE EFFECTS OF LEADERSHIP STYLE AND GROUP STRUCTURE UPON GROUP PERFORMANCE (1977) (11)
Enumeration of self-converse digraphs (1966) (11)
Decompositions of complete symmetric digraphs into the four oriented quadrilaterals (1978) (11)
Note on Carnap's relational asymptotic relative frequencies (1958) (11)
STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY1 (1977) (11)
An Elementary Theorem on Graphs (1959) (11)
On the Core of a Graph (1967) (11)
The cohesiveness of a point of a graph (1981) (11)
On the number of balanced signed graphs. (1967) (11)
LUNE-FREE KNOT GRAPHS (2005) (11)
On Indecomposable Graphs (1967) (11)
A Symmetric Strategy in Graph Avoidance Games (2001) (10)
The Irregularity Cost of a Graph (1997) (10)
A Very Independent Axiom System (1961) (10)
A graph and its complement with specified properties. III: Girth and circumference. (1979) (10)
A Very Independent Axiom System (1961) (10)
Generalized ramsey theory VIII. The size ramsey number of small graphs (1983) (10)
Anticritical graphs (1976) (10)
Structural models in anthropology: CAMBRIDGE STUDIES IN SOCIAL ANTHROPOLOGY (1984) (10)
THE POWER GROUP OF TWO PERMUTATION GROUPS. (1965) (10)
Chemical graphs. IX. Isotope‐isomerism of multiply‐labelled compounds (1970) (10)
Spanning subgraphs of a hypercube IV: Rooted trees (1993) (9)
The probability that a point of a tree is fixed (1979) (9)
Anatomy of a Communication Arc (1972) (9)
The Two-Triangle Case of the Acquaintance Graph (1972) (9)
Local Restrictions for Various Classes of Directed Graphs (1965) (9)
Topicity of vertices and edges in the möbius ladders: a topological result with chemical implications (1988) (9)
Isomorphic factorizations VIII: Bisectable trees (1984) (9)
The neighborhood inclusion structure of a graph (1993) (9)
Graphs Suppressible to an Edge (1972) (9)
The smallest 2-connected cubic bipartite planar nonhamiltonian graph (1982) (9)
Product Graphs are Sum Graphs (1992) (9)
A tribute to Frank P. Ramsey, 1903-1930 (1983) (8)
Twenty-step algorithm for determining the asymptotic number of trees of various species: corrigenda (1986) (8)
A graph and its complement with specified properties. VI. Chromatic and achromatic numbers. (1983) (8)
Generalized Ramsey theory for graphs XII: Bipartite Ramsey sets (1981) (8)
The irregularity cost or sum of a graph (1993) (8)
Spanning subgraphs of a hypercube II: Double starlike trees (1988) (8)
The class reconstruction number of maximal planar graphs (1987) (8)
Cubical graphs and cubical dimensions (1988) (8)
Node-graceful graphs (1988) (8)
A Maximal Toroidal Graph which is not a Triangulation. (1973) (8)
Demiarcs: An atomistic approach to relational systems and group dynamics (1971) (8)
On the automorphism group of a matroid (1972) (7)
Convexity in Graphs: Achievement and Avoidance Games (1984) (7)
Cycle Basis Interpolation Theorems (1985) (7)
A Linear Algorithm for the Cutting Center of a Tree (1986) (7)
Unicyclic realizability of a degree list (1978) (7)
On the Computational Complexity of the Forcing Chromatic Number (2004) (7)
Point Arboricity Critical Graphs Exist (1975) (7)
PÓLYA'S THEOREM (1973) (7)
A Radio Coloring of a Hypercube (2002) (7)
The Number of Lines in a Digraph of Each Connectedness Category (1961) (7)
Which Graphs have only Self-Converse Orientations? (1967) (7)
Parallel concepts in graph theory (1993) (7)
Unsolved Problems on Distance in Graphs (2002) (7)
A graph and its complement with specified properties V: The self-complement index (1980) (7)
Destroying symmetry by orienting edges: Complete graphs and complete bigraphs (2001) (7)
An achievement game on a toroidal board (1983) (7)
A Study of Maximum Unit-circle Caterpillars - Tools for the Study of the Shape of Adsorption Patterns (1996) (7)
INDEPENDENT DISCOVERIES IN GRAPH THEORY * (1979) (7)
Generalized ramsey theory XV: Achievement and avoidance games for bipartite graphs (1984) (6)
Embedding and characterization of quantum chemical reaction graphs on two-dimensional orientable surfaces (1988) (6)
The rediscovery of Redfield's papers (1984) (6)
The curl of graphs and networks (1985) (6)
The graphs for which all strong orientations are hamiltonian (1979) (6)
The diet transform of lattice patterns, equivalence relations, and similarity measures (1996) (6)
On the embedding of complete graphs in orientable surfaces (1963) (6)
The Minimum Spanning Tree Problem in Archaeology (1996) (6)
Vulnerability in graphs of diameter four (1993) (6)
Graphs whose radio coloring number equals the number of nodes (1999) (6)
A note on Freud's 'instincts and their vicissitudes'. (1959) (6)
On the galactic number of a hypercube (1988) (6)
STRUCTURAL MODELS AND GRAPH THEORY (1981) (6)
The subcircuit extraction problem (2003) (6)
On the Maximum Value of the Maximum Degree of Kinematic Chains (1987) (6)
Connect-it Games (1984) (6)
A Graphical Exposition of the Ising Problem (1971) (6)
Some Small Sized Spanning Subgraphs of a Hypercube (1997) (5)
Realizing the chromatic numbers of triangulations of surfaces (1993) (5)
Generalized Ramsey theory. IX. Isomorphic factorizations. IV. Isomorphic Ramsey numbers. (1979) (5)
The color cost of a caterpillar (1997) (5)
The probability of a given 1-choice structure (1966) (5)
Boolean distance for graphs (1982) (5)
Arrow Diagrams are Line Digraphs (1968) (5)
A COMPLEMENTARY PROBLEM ON NONPLANAR GRAPHS (1962) (5)
ON THE NUMBER OF DISSIMILAR LINE-SUBGRAPHS OF A GIVEN GRAPH (1956) (5)
The e-mail gossip number and the connected domination number☆ (1997) (5)
Achievement and avoidance games designed from theorems (1981) (5)
Self-Complementary Generalized Orbits of a Permutation Group (1974) (5)
On Degree Achievement and Avoidance Games for Graphs (1987) (5)
Computer-aided analysis of monotonic sequence games (1983) (5)
Some Properties of n-Adic Relations (1956) (5)
Chapter 4 – GRAPHS (1973) (5)
On the point-group and line-group of a graph (1968) (5)
Cutpoints in the conjunction of two graphs (1978) (5)
The concept of negative information (1978) (5)
A matrix algorithm for solutions and r‐bases of a finite irreflexive relation (1959) (5)
The divisibility theorem for isomorphic factorizations of complete graphs (1977) (5)
On the Number of Unique Subgraphs (1973) (5)
Some problems in topological graph theory (1980) (5)
The Integral of a Tree (1988) (4)
Trees and Unicyclic Graphs (1967) (4)
Some genuine graph models in anthropology (1986) (4)
One node fault tolerance for caterpillars and starlike trees (1995) (4)
Algorithms for derivation of structurally stable Hamiltonian signed graphs (2004) (4)
A Test of Communication and Cultural Similarity in Polynesian Prehistory (1998) (4)
Enumeration under group action: Unsolved graphical enumeration problems, IV (1970) (4)
Monotone sequences of graphical invariants (1980) (4)
On eccentricity sequences of connected graphs (2009) (4)
A graph-theoretic approach to the analysis of international relations (1970) (4)
Consistency Theory is Alive and Well (1983) (4)
On The Line-Group of Two-Terminal Series-Parallel Networks (1959) (4)
Note on an enumeration theorem of Davis and Slepian. (1955) (4)
On clique-extremal (p, q)-graphs (1974) (4)
The dissimilarity characteristic of linear graphs (1954) (4)
Minimum degree games for graphs (1994) (4)
Atomic Boolean-like rings with finite radical (1950) (4)
The bichromaticity of a tree (1978) (4)
Identity orientation of complete bipartite graphs (2005) (4)
The logical structure of asymmetric marriage systems (1996) (3)
Note on the Pólya and Otter formulas for enumerating trees. (1955) (3)
On balance in group graphs (1982) (3)
Breaking Symmetry in Complete Graphs by Orienting Edges: Asymptotic Bounds (1998) (3)
The Paris Metro: Is Its Graph Planar? (1994) (3)
Recent results in topological graph theory (1964) (3)
An Eigenvector Characterization of Cospectral Graphs Having Cospectral Joins a (1989) (3)
Labeled trees with unlabeled end-points (1969) (3)
Close-Proximity Analysis: Another Variation on the Minimum-Spanning-Tree Problem (1995) (3)
Graph Theoretic Models (1980) (3)
DOMINATION ALTERATION SET!3 IN GRAPHS (1983) (3)
A Mathematical Approach to Nonfigurative Modular Pictures (1976) (3)
Regular Digraphs Containing a Given Digraph (1984) (3)
A Characterization of Implicative Boolean Rings (1953) (3)
The adjacency graphs of a complex (1976) (3)
GRAPHICAL CONFLICT I: A NEW CLASS OF EXTREMAL PROBLEMS (1979) (3)
Which directed graphs have a solution (1977) (3)
The Shields-Harary indices of vulnerability of a graph (2001) (3)
Every forest can be obtained from a minimal block. (1981) (3)
A Parity Relation Partitions its Field Distinctly (1961) (3)
Demiarcs, Creaons and Genons (1981) (3)
Homage to roberto frucht (1982) (3)
On Defining Sets Of Vertex Colorings Of The Cartesian Product Of A Cycle With A Complete Graph M (1996) (3)
Smallest cubic and quartic graphs with a given number of cutpoints and bridges (1982) (3)
Review: John Riordan, An introduction to combinatorial analysis (1959) (3)
On the planarity of 2-complexes (1976) (3)
Class reconstruction numbers of unicyclic graphs (1988) (2)
The minimal blocks of diameter two and three (1977) (2)
A new graph characteristic and its application to numerical computability (2001) (2)
Graph Theory in Modern Engineering (Ernest J. Henley and R. A. Williams) (1974) (2)
On the Number of Dissimilar Graphs Between a Given Graph-Subgraph Pair (1958) (2)
On the regulation number of a multigraph (1985) (2)
Hypercubes, shuffle-exchange graphs and de Bruijn digraphs (1993) (2)
POWER GROUP ENUMERATION (1973) (2)
How large can the domination numbers of a graph be? (2000) (2)
The Edge-Distinguishing Chromatic Number of Paths and Cycles (1988) (2)
On "The Tantalizer" and "Instant Insanity" (1977) (2)
The degree sets of connected infinite graphs (1983) (2)
Corrections: Generalized Ramsey Theory for Graphs V (1975) (2)
Hierarchical Opposition Revisited: Reply (1996) (2)
Characterization of $(r,\,s)$-adjacency graphs of complexes (1981) (2)
Graph theory as applied mathematics (1986) (2)
Realization of Parity Visits in Walking a Graph (1985) (2)
An Intuitive Approach to Interval Numbers of Graphs (1980) (2)
Variations on the golden rule (1982) (2)
Graphs and Combinatorics (1974) (2)
Quantifying fault recovery in multiprocessor systems (1993) (2)
On the lengths of symmetry breaking-preserving games on graphs (2004) (2)
Sum Graphs and Geographic Information (1993) (2)
Minimal blocking flow in networks (1986) (2)
Homage to George Pólya (1977) (2)
The graph of a boolean function (1990) (2)
Minimum maximal graphs with forbidden subgraphs (1985) (2)
Kinship, Networks, and Exchange: Applications of the Minimum Spanning Tree Problem to Network Analysis (1998) (2)
The number of dissimilar supergraphs of a linear graph. (1957) (2)
Covering and packing in graphs—V: Mispacking subcubes in hypercubes (1988) (2)
Island networks: Conclusion (1996) (2)
THE EXTENSION OF AN ARBITRARY BOOLEAN ALGEBRA TO AN IMPLICATIVE BOOLEAN ALGEBRA (1953) (2)
Chapter 9 – ASYMPTOTICS (1973) (2)
Proof techniques in graph theory : proceedings of the second Ann Arbor Graph Theory Conference, February 1968 (1969) (2)
Generalized ramsey theory for graphs VII: Ramsey numbers for multigraphs and networks (1978) (2)
The theory of tournaments: A miniature mathematical system (1966) (1)
THE EXPLOSIVE GROWTH OF GRAPH THEORY (1979) (1)
Island networks: Centrality (1996) (1)
Degree Sequences of Infinite Graphs (1981) (1)
On complete systems of invariants for small graphs (1997) (1)
Correction and Addendum to "A Dual form of Kuratowski's Theorem" (1965) (1)
On the point linear arboricity of a graph (1991) (1)
Graphs and combinatorics : proceedings of the Capital Conference on Graph Theory and Combinatorics at the George Washington University, June 18-22, 1973 (1974) (1)
The Reconstruction Conjecture for Balanced Signed Graphs (1985) (1)
Homage to the memory of Kazimierz Kuratowski (1981) (1)
A Point-Symmetric Graph that is Nowhere Reversible (1982) (1)
Graphical Completions of a Sequence (1980) (1)
Recent results on graphical enumeration (1974) (1)
To the Memory of Clyde Tombaugh, 1906-1997 (1997) (1)
A Simple Criterion for a Graph to have a Perfect Matching (1987) (1)
Adventures with Ramsey Theory (Graphs and Combinatorics III) (1980) (1)
Oedipus loves his mother (1982) (1)
Graph theory 1736-1936 : By N. L. Biggs, E. K. Lloyd, and R. J. Wilson. Oxford (Clarendon Press). 1976. 239 pp. $27.85 (1977) (1)
Collective Geodesics and Co-evolution : A Graph Theoretic Structural Model (2002) (1)
The Trail Number of a Graph (1982) (1)
What Are Mathematical Models and What Should They Be (1992) (1)
The bichromaticity of a lattice-graph (1977) (1)
On the ABC of graph applications (1991) (1)
CMOS IC Topology Design Verification by Heuristic Dynamic Programming (HDP) (2002) (1)
On meshy trees (1989) (1)
On complete atomic proper relation algebras (1950) (1)
Applications of Graph Theory to Group Structure (Claude Flament) (1964) (1)
Edge Sums Of De Bruijn Interconnection Networks (2003) (1)
Island networks: The minimum spanning tree problem (1996) (1)
Recent results on trees (1974) (1)
A MEASURE OF AXIOMATIC INDEPENDENCE (1963) (1)
On the Group of a Graph with Respect To a Subgraph (1958) (1)
The Bridges of Königsberg/Kaliningrad: A Tale of One City (2001) (1)
13. On the bipartite distribution of phonemes (2002) (1)
The Pólya Picture Album—Encounters of a Mathematician. Edited by Gerald L. Alexanderson (1989) (1)
In memory of Torrence Parsons, 1941-1987 (1988) (0)
The number of archiral trees. (1975) (0)
NODE CONNECTIVITY AND CONDITIONAL DENSITY– D. White and F. Harary Definitions of Cohesive Sets in Social Networks (2001) (0)
On the Maximum Number of Cyclic Triples in Oriented Graphs (2001) (0)
Counting circular caterpillars (1995) (0)
On the Evolution of Square-cell Animals (2005) (0)
A NOTE ON EVALUATING DETERMINANTS (1960) (0)
Structural models in anthropology: Graph theory and anthropology (1984) (0)
Island networks: Trees (1996) (0)
Some graph theoretic models in literary and linguistic research (1985) (0)
Abstract of 'Graph Theory and Electric Networks II' (1960) (0)
On Tactical Configurations with No Four-Cycles (1976) (0)
NLY SELKDUAL SIGNINGS (1979) (0)
Chapter 5 – DIGRAPHS (1973) (0)
Preface: Graph theoretic models in computer science II (1993) (0)
The Automorphism Group of a Hypercube 1 (0)
GRAPHICAL P ROPERTIES O F P OLYHEXES: P ERFECT M ATCHING VECTOR A ND F ORCING (1991) (0)
A constraint logic programming approach for generating all perfect matchings (2002) (0)
THE UNIQUE 2-EDGE-COLOURING OF K6 WHICH PRODUCES EXACTLY TWO MONOCHROMATICQUADRILATERALS (1997) (0)
The subcircuit extraction problem - Potentials, IEEE (2001) (0)
Research Activities in Graph Theory. (1973) (0)
ERRATUM TO "CHARACTERIZATION OF (r, s)-ADJACENCY GRAPHS OF COMPLEXES" (1982) (0)
Chapter 7 – SUPERPOSITION (1973) (0)
The PM22I Interconnection Network (1989) (0)
The graphs with only self-dual signings (1979) (0)
Closure to “Discussion of ‘On the Maximum Value of the Maximum Degree of Kinematic Chains’” (1987, ASME J. Mech. Transm. Autom. Des., 109, p. 490) (1987) (0)
Communication Conflict (1981) (0)
GRAPH THEORETIC METHODS IN THE MANAGEMENT SCIENCES*1 (1977) (0)
Structural models in anthropology: References (1984) (0)
Which graphs are pluperfect? (1993) (0)
Island networks: Search trees: II (1996) (0)
Flyer of Graph Theory and Geography, Wiley. (2002) (0)
Oriented two-dimensional circuits (1981) (0)
THE NUMBER OF LINEAR, DIRECTED, ROOTED, (2010) (0)
Editorial: Changing of the guard (1986) (0)
Early Computer Science Adventures of a Mathematician (2001) (0)
An exact value for the path-chromatic index of a complete graph (1991) (0)
Remark on the Preceding Note (1962) (0)
ON THE DICHROMATIC INDEX OF A DIGRAPH (1996) (0)
ON A HILBERT SPACE WITH NONASSOCIATIVE SCALARS (0)
Review: Karl Egil Aubert, On the Foundation of the Theory of Relations and the Logical Independence of Generalized Concepts of Reflexivity, Symmetry and Transitivity (1954) (0)
The Geometric Dual of a Graph a (1989) (0)
Structural models in anthropology: Networks (1984) (0)
On the Algebraic Structure of Knots (1949) (0)
Editorial (1977) (0)
Program of Scientific Activity of the Catania Combinatorial Group (2003) (0)
On the point-core of a graph (1966) (0)
Title : Exchange in Oceania : A Graph Theoretic Analysis (2009) (0)
Line minimal Boolean forests (1977) (0)
Some Problems in Topographical Graph Theory (1980) (0)
Island networks: Island networks and graphs (1996) (0)
Variations on the Ising problem (1986) (0)
Structural models in anthropology: Graphs and groups (1984) (0)
On the Structure of a Triangle-Free Infinite-Chromatic Graph of Gyarfas (1983) (0)
Problems for Solution: 4533-4537 (1953) (0)
Island networks: References (1996) (0)
Logic foundations of kinematic chains : graphs, line graphs, and hypergraphs (1990) (0)
An investigation of hypercube invariants (1989) (0)
Cardinality of Finite Topologies (2006) (0)
Old intelligencer (1985) (0)
Chapter 10 – UNSOLVED PROBLEMS (1973) (0)
Los Angeles, 1994--A Spatial Scientific View (1994) (0)
The di erence between a graph and itssquareDonald Aingworth (2007) (0)
Chapter 3 – TREES (1973) (0)
Chapter 8 – BLOCKS (1973) (0)
Applied Graph Theory (W. K. Chen) (1973) (0)
Correction: “The smallest graph whose group is cyclic” (1972) (0)
Enumeration of Finite Automata 1 (2004) (0)
In praise of paul erdös on his seventieth (1983) (0)
Variations on a hypercube: Embellishments of parallel architectures (1993) (0)
An Heuristic Algorithm for Handling Multiple Responses (2000) (0)
GRAPH THE RETIC MODELS (1980) (0)
Permutations with Restricted Position (1962) (0)
Examples and Counterexamples in Graph Theory (Michael Capobianco and John C. Molluzzo) (1983) (0)
On the codomination number of a graph (1993) (0)
Island networks: Digraphs (1996) (0)
Tengbe rgen, and Kruyswijk (2006) (0)
Graph Theory with Applications to Air Force Systems. (1975) (0)
Erratum to: “Characterization of (,)-adjacency graphs of complexes” [Proc. Amer. Math. Soc. 83 (1981), no. 1, 211–214; MR 83a:05113] (1982) (0)
Structural models in anthropology: Digraphs (1984) (0)
Foreword by J. A. Barnes (1984) (0)
BIBLIOGRAPHY: GRAPH THEORY AND COMBINATORIAL THEORY. (1967) (0)

This paper list is powered by the following services:

Other Resources About Frank Harary

What Schools Are Affiliated With Frank Harary?

Frank Harary is affiliated with the following schools:

Frank Harary's Academic­Influence.com Rankings

Frank Harary's Degrees

Similar Degrees You Can Earn

Why Is Frank Harary Influential?

Frank Harary's Published Works

Published Works

Other Resources About Frank Harary

What Schools Are Affiliated With Frank Harary?

Frank Harary's AcademicInfluence.com Rankings