Pentavalent symmetric graphs of order four times an odd square-free integer - Ling, Bo (Ars mathematica contemporanea, 2019)
A graph is said to be symmetric if its automorphism group is transitive on its arcs. S.-T. Guo et al. Electron. J. Comb. 18, No. 1, Research Paper P233, 13 p. (2011) and J. Pan et al. Electron. J. Comb. 20, No. 1, Research Paper P36, 9 p. (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 such graph ?$Γ$?, either the full automorphism group ?$AutΓ$? is isomorphic to ?$PSL(2, p)$?, ?$PGL(2, p)$?, ?$PSL(2, p) × \mathbb{Z}_2$? or ?$PGL(2, p) × \mathbb{Z}_2$?, or ?$Γ$? is isomorphic to one of 9 graphs.
Keywords: arc-transitive graphs; automorphism group; grupa avtomorfizmov; ločno-tranzitiven graf; normal quotient; normalni kvocient