Finite hexavalent edge-primitive graphs

摘要

Weiss (1973) determined all cubic edge-primitive graphs, and Guo, Feng and Li recently determined all tetravalent and pentavalent edge-primitive graphs (notice that their method is difficult to treat the bigger valency case because the edge stabilizers may be insoluble). In this paper, we study hexavalent edge-primitive graphs by using line graphs. The s-arc-transitivity of such graphs are determined, and the automorphism groups of such graphs besides K6,6 are proved to be almost simple. Two families of hexavalent edge-primitive graphs are also completely determined.