科研之友
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摘要
A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive, but not vertex-transitive. Every semisymmetric graph is a bipartite graph with two biparts of equal size. It was proved by Folkman in (J Comb Theory Ser B 3:215-232, 1967) that there exist no semisymmetric graphs of order and , where is a prime. For any distinct primes and , the classification of semisymmetric graphs of order was given by Du and Xu in (Comm Algebra 28:2685-2715, 2000). Naturally, one of our long-term goals is to determine all the semisymmetric graphs of order , for any prime . All these graphs are divided into two subclasses: (I) the automorphism group acts unfaithfully on at least one bipart; and (II) acts faithfully on both biparts. In Wang and Du (Eur J Comb 36:393-405, 2014), a group theoretical characterization for Subclass (I) was given by the authors. Based on this characterization, this paper gives a complete classification for Subclass (I).
