Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9512145 | Discrete Mathematics | 2005 | 7 Pages |
Abstract
Let Cay(G,S) be a connected tetravalent Cayley graph on a regular p-group G and let Aut(G) be the automorphism group of G. In this paper, it is proved that, for each prime pâ 2,5, the automorphism group of the Cayley graph Cay(G,S) is the semidirect product R(G)âAut(G,S) where R(G) is the right regular representation of G and Aut(G,S)={αâAut(G)|Sα=S}. The proof depends on the classification of finite simple groups. This implies that if pâ 2,5 then the Cayley graph Cay(G,S) is normal, namely, the automorphism group of Cay(G,S) contains R(G) as a normal subgroup.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yan-Quan Feng, Ming-Yao Xu,