Finite hexavalent edge-primitive graphs

Cixuan Wu and Jiangmin Pan

Applied Mathematics and Computation, 2020, vol. 378, issue C

Abstract: 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.

Keywords: Edge-primitive graph; Line graph; Edge stabilizer; S-Transitive graph (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301764

DOI: 10.1016/j.amc.2020.125207

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