On symmetric graphs of order four times an odd square-free integer and valency seven

A graph is called symmetric if its automorphism group is transitive on its arcs. In this paper, we classify symmetric graphs of order four times an odd square-free integer and valency seven. It is shown that, either the graph is isomorphic to one of 9 specific graphs or its full automorphism group i...

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Bibliographic Details
Published in:Discrete mathematics 2017-09, Vol.340 (9), p.2071-2078
Main Authors: Pan, Jiangmin, Ling, Bo, Ding, Suyun
Format: Article
Language:English
Subjects:
Automorphism group
Normal quotient graph
Symmetric graph
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Summary:A graph is called symmetric if its automorphism group is transitive on its arcs. In this paper, we classify symmetric graphs of order four times an odd square-free integer and valency seven. It is shown that, either the graph is isomorphic to one of 9 specific graphs or its full automorphism group is isomorphic to PSL(2,p), PGL(2,p), PSL(2,p)×Z2 or PGL(2,p)×Z2 with p≡±1(mod7) a prime.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2017.04.008