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Finite hexavalent edge-primitive graphs

Author

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  • Wu, Cixuan
  • Pan, Jiangmin

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.

Suggested Citation

  • Wu, Cixuan & Pan, Jiangmin, 2020. "Finite hexavalent edge-primitive graphs," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301764
    DOI: 10.1016/j.amc.2020.125207
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