2017/02/19 by Ling, Bo, Lou, Ben Gong, Wu, Ci Xuan
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1702.05750
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 \itΓ, either the full automorphism group \sf Aut\itΓ is isomorphic to \sf PSL(2,p), \sf PGL(2,p), \sf PSL(2,p)×ℤ2 or \sf PGL(2,p)×ℤ2, or \itΓ is isomorphic to one of 8 graphs.