Some Basic Definitions in Graph Theory

JOHN W. ESSAM; MICHAEL E. FISHER

doi:10.1103/RevModPhys.42.272

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Some Basic Definitions in Graph Theory

JOHN W. ESSAM^* and MICHAEL E. FISHER

JOHN W. ESSAM^*

Applied Mathematics Department, Brookhaven National Laboratory, Upton, Long Island, New York 11973

MICHAEL E. FISHER

Baker Laboratory, Cornell University, Ithaca, New York 14850

^*On leave from Department of Mathematics, Westfield College, London N.W. 3, England.

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Rev. Mod. Phys. 42, 272 – Published 1 April, 1970

DOI: https://doi.org/10.1103/RevModPhys.42.272

Abstract

A systematic list of definitions of some basic concepts in graph theory of application to physics is presented. An index, some illustrative theorems, and a brief bibliography are included.

References (9)

Berge, C., Theorie des Graphes et ses Applications (Dunod et Cie, Paris, 1958) Berge, C.English translation: The Theory of Graphs (Methuen and Co., London, 1962)
Busacker, R. G., and T. L. Saaty, Finite Graphs and Networks (McGraw-Hill Book Co., Inc., New York, 1965)
Kasteleyn, P. W., "Graph Theory and Crystal Physics," in the Proceedings of the 1963 NATO Summer School: Graph Theory and Theoretical Physics, F. Harary, Ed. (Academic Press Inc., New York, 1967)
Harary, F., Graph Theory (Addison-Wesley Publ. Co., Inc., 1969)
Ore, O., Theory of Graphs (American Mathematical Society, Providence, R.I., 1962), Vol. 38, Am. Math. Soc. Colloq. Publications
Stell, G., "Cluster Expansions for Classical Systems in Equilibrium," in The Equilibrium Theory of Classical Fluids, H. L. Frisch and J. L. Lebowitz, Eds. (W. A. Benjamin, Inc., New York, 1964)
Sykes, M. F., J. W. Essam, B. R. Heap, and B. J. Hiley, "Lattice Constant Systems and Graph Theory," J. Math. Phys. 7, 1557 (1966)
Tutte, W. T., Connectivity in Graphs (University of Toronto Press, Toronto, Ontario, Can., 1966)
Uhlenbeck, G. E., and G. W. Ford, "The Theory of Linear Graphs with Applications to the Theory of the Virial Development of the Properties of Gases," in Studies in Statistical Mechanics, J. de Boer and G. E. Uhlenbeck, Eds. (North-Holland Publ Co., Amsterdam, 1962), Vol. I

[c1] Berge, C., Theorie des Graphes et ses Applications (Dunod et Cie, Paris, 1958) Berge, C.English translation: The Theory of Graphs (Methuen and Co., London, 1962)

[c2] Busacker, R. G., and T. L. Saaty, Finite Graphs and Networks (McGraw-Hill Book Co., Inc., New York, 1965)

[c3] Kasteleyn, P. W., "Graph Theory and Crystal Physics," in the Proceedings of the 1963 NATO Summer School: Graph Theory and Theoretical Physics, F. Harary, Ed. (Academic Press Inc., New York, 1967)

[c4] Harary, F., Graph Theory (Addison-Wesley Publ. Co., Inc., 1969)

[c5] Ore, O., Theory of Graphs (American Mathematical Society, Providence, R.I., 1962), Vol. 38, Am. Math. Soc. Colloq. Publications

[c6] Stell, G., "Cluster Expansions for Classical Systems in Equilibrium," in The Equilibrium Theory of Classical Fluids, H. L. Frisch and J. L. Lebowitz, Eds. (W. A. Benjamin, Inc., New York, 1964)

[c7] Sykes, M. F., J. W. Essam, B. R. Heap, and B. J. Hiley, "Lattice Constant Systems and Graph Theory," J. Math. Phys. 7, 1557 (1966)

[c8] Tutte, W. T., Connectivity in Graphs (University of Toronto Press, Toronto, Ontario, Can., 1966)

[c9] Uhlenbeck, G. E., and G. W. Ford, "The Theory of Linear Graphs with Applications to the Theory of the Virial Development of the Properties of Gases," in Studies in Statistical Mechanics, J. de Boer and G. E. Uhlenbeck, Eds. (North-Holland Publ Co., Amsterdam, 1962), Vol. I

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Some Basic Definitions in Graph Theory

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