Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903025 | Discrete Mathematics | 2018 | 7 Pages |
Abstract
Let Î be a graph and let G be a group of automorphisms of Î. The graph Î is called G-normal if G is normal in the automorphism group of Î. Let T be a finite non-abelian simple group and let G=Tl with lâ¥1. In this paper we prove that if every connected pentavalent symmetric T-vertex-transitive graph is T-normal, then every connected pentavalent symmetric G-vertex-transitive graph is G-normal. This result, among others, implies that every connected pentavalent symmetric G-vertex-transitive graph is G-normal except T is one of 57 simple groups. Furthermore, every connected pentavalent symmetric G-regular graph is G-normal except T is one of 20 simple groups, and every connected pentavalent G-symmetric graph is G-normal except T is one of 17 simple groups.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jia-Li Du, Yan-Quan Feng,