Graph Theory and Computing

Graph Theory and Computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. Discussions focus on numbered graphs and difference sets, Euclidean models and complete graphs, classes and conditions for graceful graphs, and maximum matching problem. The manuscript then elaborates on the evolution of the path number of a graph, production of graphs by computer, and graph-theoretic programming language. Topics include FORTRAN characteristics of GTPL, design considerations, representation and identification of graphs in a computer, production of simple graphs and star topologies, and production of stars having a given topology. The manuscript examines the entropy of transformed finite-state automata and associated languages; counting hexagonal and triangular polyominoes; and symmetry of cubical and general polyominoes. Graph coloring algorithms, algebraic isomorphism invariants for graphs of automata, and coding of various kinds of unlabeled trees are also discussed. The publication is a valuable source of information for researchers interested in graph theory and computing. Content: CONTRIBUTORS, Page ii Front Matter, Page iii Copyright, Page iv LIST OF CONTRIBUTORS, Pages xi-xii PREFACE, Pages xiii-xiv ALTERNATING CHAIN METHODS: A SURVEY, Pages 1-13, Claude Berge THE AVERAGE HEIGHT OF PLANTED PLANE TREES, Pages 15-22, N.G. de Bruijn, D.E. Knuth, S.O. Rice HOW TO NUMBER A GRAPH, Pages 23-37, Solomon W. Golomb EVOLUTION OF THE PATH NUMBER OF A GRAPH: COVERING AND PACKING IN GRAPHS, II, Pages 39-45, Frank Harary, Allen J. Schwenk THE PRODUCTION OF GRAPHS BY COMPUTER, Pages 47-62, B.R. Heap A GRAPH-THEORETIC PROGRAMMING LANGUAGE, Pages 63-75, C.A. King ENTROPY OF TRANSFORMED FINITE-STATE AUTOMATA AND ASSOCIATED LANGUAGES, Pages 77-86, W. Kuich COUNTING HEXAGONAL AND TRIANGULAR POLYOMINOES, Pages 87-100, W.F. Lunnon SYMMETRY OF CUBICAL AND GENERAL POLYOMINOES, Pages 101-108, W.F. Lunnon GRAPH COLORING ALGORITHMS, Pages 109-122, David W. Matula, George Marble, Joel D. Isaacson ALGEBRAIC ISOMORPHISM INVARIANTS FOR GRAPHS OF AUTOMATA, Pages 123-152, John F. Meyer THE CODING OF VARIOUS KINDS OF UNLABELED TREES, Pages 153-182, Ronald C. Read A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS, Pages 183-217, Donald J. Rose INTELLIGENT GRAPHS: NETWORKS OF FINITE AUTOMATA CAPABLE OF SOLVING GRAPH PROBLEMS, Pages 219-265, P. Rosenstiehl, J.R. Fiksel, A. Holliger AN ALGORITHM FOR A GENERAL CONSTRAINED SET COVERING PROBLEM, Pages 267-283, B. Roy TRIPARTITE PATH NUMBERS, Pages 285-294, R.G. Stanton, L.O. James, D.D. Cowan NON-HAMILTONIAN PLANAR MAPS, Pages 295-301, W.T. Tutte A TOP-DOWN ALGORITHM FOR CONSTRUCTING NEARLY OPTIMAL LEXICOGRAPHIC TREES, Pages 303-323, W.A. Walker, C.C. Gotlieb INDEX, Pages 325-329