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

Yang, Liting; Li, Yali

doi:10.3390/math14091448

Open AccessArticle

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

by

Liting Yang

and

Yali Li

^*

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

^*

Author to whom correspondence should be addressed.

Mathematics 2026, 14(9), 1448; https://doi.org/10.3390/math14091448

Submission received: 31 March 2026 / Revised: 17 April 2026 / Accepted: 21 April 2026 / Published: 25 April 2026

(This article belongs to the Special Issue New Perspectives of Graph Theory and Combinatorics)

Download Versions Notes

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.

Keywords: Cayley graph; 1-regular; core-free; automorphism group

Share and Cite

MDPI and ACS Style

Yang, L.; Li, Y. Classification of 14-Valent 1-Regular Core-Free Cayley Graphs. Mathematics 2026, 14, 1448. https://doi.org/10.3390/math14091448

AMA Style

Yang L, Li Y. Classification of 14-Valent 1-Regular Core-Free Cayley Graphs. Mathematics. 2026; 14(9):1448. https://doi.org/10.3390/math14091448

Chicago/Turabian Style

Yang, Liting, and Yali Li. 2026. "Classification of 14-Valent 1-Regular Core-Free Cayley Graphs" Mathematics 14, no. 9: 1448. https://doi.org/10.3390/math14091448

APA Style

Yang, L., & Li, Y. (2026). Classification of 14-Valent 1-Regular Core-Free Cayley Graphs. Mathematics, 14(9), 1448. https://doi.org/10.3390/math14091448

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

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

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI