科研之友
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摘要
In this paper, we study arc-transitive pentavalent graphs of order 4p(n) with p a prime and n a positive integer. It is proved that no such graph exists for each prime p >= 5, and all such graphs with p = 2 or 3 which are G-basic (that is, G has no non-trivial normal subgroup such that the graph is a normal cover of the corresponding normal quotient graph) are determined. Moreover, as an application, arc-transitive pentavalent graphs of order 4p(2) and 4p(3) are determined.
