Geodesic
A classification of semisymmetric graphs of order $2p^3$: unfaithful case
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 275-302.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 J. Folkman [J. Comb. Theory 3, 215--232 (1967; Zbl 0158.42501)] that there exist no semisymmetric graphs of order $2p$ and $2p^2$, where $p$ is a prime. For any distinct primes $p$ and $q$, the classification of semisymmetric graphs of order $2pq$ was given by S. F. Du and M. Y. Xu [Commun. Algebra 28, No. 6, 2685--2715 (2000; Zbl 0944.05051)]. Naturally, one of our long-term goals is to determine all the semisymmetric graphs of order $2p^3$, for any prime $p$. All these graphs $\Gamma $ are divided into two subclasses: (I) the automorphism group Aut $\Gamma$ acts unfaithfully on at least one bipart; and (II) Aut $(\Gamma )$ acts faithfully on both biparts. In L. Wang and S. F. Du [Eur. J. Comb. 36, 393--405 (2014; Zbl 1284.05116)], 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).
Classification : 05C25
Keywords: permutation group, vertex-transitive graph, semisymmetric graph 
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     title = {A classification of semisymmetric graphs of order $2p^3$: unfaithful case},
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Du, Shaofei; Wang, Li. A classification of semisymmetric graphs of order $2p^3$: unfaithful case. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 275-302. http://geodesic.mathdoc.fr/item/JAC_2015__41_2_a9/