Graph Symmetry: Algebraic Methods and Applications (NATO Science Series C: (closed))
By Gena Hahn, Gert Sabidussi
* Publisher: Springer
* Number Of Pages: 444
* Publication Date: 1997-06-30
* ISBN-10 / ASIN: 0792346688
* ISBN-13 / EAN: 9780792346685
* Binding: Hardcover
Product Description:
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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