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arXiv · 1702.05750

Pentavalent symmetric graphs of order four times an odd square-free integer

Bo Ling·Ben Gong Lou·Ci Xuan Wu
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Abstract

A graph is said to be symmetric if its automorphism group is transitive on its arcs. Guo et al. (Electronic J. Combin. 18, \#P233, 2011) and Pan et al. (Electronic J. Combin. 20, \#P36, 2013) determined all pentavalent symmetric graphs of order $4pq$. In this paper, we shall generalize this result by determining all connected pentavalent symmetric graphs of order four times an odd square-free integer. It is shown in this paper that, for each of such graphs $\it\Gamma$, either the full automorphism group ${\sf Aut}\it\Gamma$ is isomorphic to ${\sf PSL}(2,p)$, ${\sf PGL}(2,p)$, ${\sf PSL}(2,p){\times}\mathbb{Z}_2$ or ${\sf PGL}(2,p){\times}\mathbb{Z}_2$, or $\it\Gamma$ is isomorphic to one of 8 graphs.

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Bo Ling, Ben Gong Lou, Ci Xuan Wu. 2017-02-19. Pentavalent symmetric graphs of order four times an odd square-free integer. https://arxiv.org/abs/1702.05750

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