On Solvable Groups and Circulant Graphs

Author: Dobson E.

Source: European Journal of Combinatorics, Volume 21, Number 7, October 2000 , pp. 881-885(5)

Publisher: Academic Press

Abstract:

Let be Euler’s phi function. We prove that a vertex-transitive graph of order n, with gcd(n, (n)) = 1, is isomorphic to a circulant graph of order n if and only if Aut() contains a transitive solvable subgroup. As a corollary, we prove that every vertex-transitive graph of order n is isomorphic to a circulant graph of order n if and only if for every such ,Aut() contains a transitive solvable subgroup and n = 4, 6, or gcd(n, (n)) = 1. Copyright 2000 Academic Press

Language: English

Document Type: Research article

Affiliations: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70808, U.S.A.

Publication date: 2000-10-01

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