Graph Symmetry: Algebraic Methods and Applications by Gena HahnGraph Symmetry: Algebraic Methods and Applications by Gena Hahn

Graph Symmetry: Algebraic Methods and Applications

EditorGena Hahn

Paperback | December 4, 2010

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The last decade has seen parallel developments in computer science and combinatorics, both dealing with networks having strong symmetry properties. Both developments are centred on Cayley graphs: in the design of large interconnection networks, Cayley graphs arise as one of the most frequently used models; on the mathematical side, they play a central role as the prototypes of vertex-transitive graphs. The surveys published here provide an account of these developments, with a strong emphasis on the fruitful interplay of methods from group theory and graph theory that characterises the subject. Topics covered include: combinatorial properties of various hierarchical families of Cayley graphs (fault tolerance, diameter, routing, forwarding indices, etc.); Laplace eigenvalues of graphs and their relations to forwarding problems, isoperimetric properties, partition problems, and random walks on graphs; vertex-transitive graphs of small orders and of orders having few prime factors; distance transitive graphs; isomorphism problems for Cayley graphs of cyclic groups; infinite vertex-transitive graphs (the random graph and generalisations, actions of the automorphisms on ray ends, relations to the growth rate of the graph).
Title:Graph Symmetry: Algebraic Methods and ApplicationsFormat:PaperbackDimensions:438 pagesPublished:December 4, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048148855

ISBN - 13:9789048148851

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Table of Contents

Preface. Isomorphism and Cayley Graphs on Abelian Groups; B. Alspach. Oligomorphic Groups and Homogeneous Graphs; P.J. Cameron. Symmetry and Eigenvectors; A. Chan, C.D. Godsil. Graph Homomorphisms: Structure and Symmetry; G. Hahn, C. Tardif. Cayley Graphs and Interconnection Networks; B. Mohar. Finite Transitive Permutation Groups and Finite Vertex-Transitive Graphs; C.E. Praeger. Vertex-Transitive Graphs and Digraphs; R. Scapellato. Ends and Automorphisms of Infinite Graphs; M.E. Watkins. Index.