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Classification of 14-Valent 1-Regular Core-Free Cayley Graphs

Author

Listed:
  • Liting Yang

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, China)

  • Yali Li

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, China)

Abstract

A Cayley graph Σ = Cay ( G , S ) is called 1-regular core-free if G is core-free in some Y ⩽ Aut Σ and Aut Σ acts regularly on the set of 1-arcs of Σ . In this paper, we classify the 14-valent 1-regular core-free Cayley graphs. In particular, we discover a non-normal Cayley graph on a non-abelian simple group. That is, 14-valent 1-regular Cayley graph on the alternating group A 6 , with full automorphism group isomorphic to S 7 . To our knowledge, this is the first example of a non-normal Cayley graph on a non-abelian simple group with even valency greater than 10.

Suggested Citation

  • Liting Yang & Yali Li, 2026. "Classification of 14-Valent 1-Regular Core-Free Cayley Graphs," Mathematics, MDPI, vol. 14(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:9:p:1448-:d:1928488
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