Graph Symmetry: Algebraic Methods and Applications / Edition 1

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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).

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Editorial Reviews

Nine papers present mathematicians with parallel developments in computer science and mathematics relating to networks with strong symmetry properties, vertix-transitive graphs in graph-theoretical language, particularly their prototypical examples, Cayley graphs. Revolving around the common theme of group theory via Cayley graphs, they expose graph theorists to the combinatorial problems encountered in the design of large, highly symmetrical networks, and provide an overview of the group theoretical methods that enter into the structural classification of such networks. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780792346685
  • Publisher: Springer Netherlands
  • Publication date: 6/30/1997
  • Series: Nato Science Series C: (closed) , #497
  • Edition description: 1997
  • Edition number: 1
  • Pages: 418
  • Product dimensions: 1.06 (w) x 9.21 (h) x 6.14 (d)

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.

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