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On Isomorphisms of Finite Cayley Graphs

✍ Scribed by M. Conder; C. Heng Li

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 148 KB
Volume: 19
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0243

No coin nor oath required. For personal study only.

✦ Synopsis

A Cayley graph Cay(G, S) of a group G is called a CI-graph if whenever T is another subset of G for which Cay(G, S) ∼ = Cay(G, T ), there exists an automorphism σ of G such that S σ = T . For a positive integer m, the group G is said to have the m-CI property if all Cayley graphs of G of valency m are CI-graphs; further, if G has the k-CI property for all k ≤ m, then G is called an m-CI-group, and a |G|-CI-group G is called a CI-group. In this paper, we prove that A 5 is not a 5-CI-group, that SL(2, 5) is not a 6-CI-group, and that all finite 6-CI-groups are soluble. Then we show that a nonabelian simple group has the 4-CI property if and only if it is A 5 , and that no nonabelian simple group has the 5-CI property. Also we give nine new examples of CI-groups of small order, which were found to be CI-groups with the assistance of a computer.

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