| Graph Symmetry: Algebraic Methods and Applications 1997 Edition Contributor(s): Hahn, Gena (Editor), Sabidussi, Gert (Editor) |
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ISBN: 0792346688 ISBN-13: 9780792346685 Publisher: Springer OUR PRICE: $208.99 Product Type: Hardcover - Other Formats Published: June 1997 Annotation: 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). |
| Additional Information |
| BISAC Categories: - Mathematics | Graphic Methods - Mathematics | Discrete Mathematics - Computers | Systems Architecture - General |
| Dewey: 511.5 |
| LCCN: 97023863 |
| Series: NATO Science Series C: |
| Physical Information: 1" H x 6.14" W x 9.21" (1.75 lbs) 418 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |