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- W2950865934 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 $itGamma$, either the full automorphism group ${sf Aut}itGamma$ 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 $itGamma$ is isomorphic to one of 8 graphs." @default.
- W2950865934 created "2019-06-27" @default.
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- W2950865934 date "2017-02-19" @default.
- W2950865934 modified "2023-09-27" @default.
- W2950865934 title "Pentavalent symmetric graphs of order four times an odd square-free integer" @default.
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- W2950865934 doi "https://doi.org/10.48550/arxiv.1702.05750" @default.
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