Graph Symmetry: Algebraic Methods and Applications

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Gena Hahn, Gert Sabidussi
Springer Science & Business Media, Jun 30, 1997 - Mathematics - 418 pages
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The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
 

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Contents

Isomorphism and Cayley graphs on abelian groups
1
Oligomorphic groups and homogeneous graphs
23
Symmetry and eigenvectors
75
structure and symmetry
107
Cayley graphs and interconnection networks
167
Some applications of Laplace eigenvalues of graphs
225
Finite transitive permutation groups and finite vertextransitive graphs
277
Vertextransitive graphs and digraphs
319
Ends and automorphisms of infinite graphs
379
Index
415
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