Journal article

CLASSIFICATION OF TETRAVALENT 2-TRANSITIVE NONNORMAL CAYLEY GRAPHS OF FINITE SIMPLE GROUPS

Xin Gui Fang, Jie Wang, Sanming Zhou

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | CAMBRIDGE UNIV PRESS | Published : 2021

Abstract

A graph Γ is called (G, s)-arc-transitive if G ≤ Aut(Γ) is transitive on the set of vertices of Γ and the set of s-arcs of Γ, where for an integer s ≤ 1 an s-arc of Γ is a sequence of s + 1 vertices (v0, v1, ⋯, vs) of Γ such that vi-1 and vi are adjacent for 1 ≤ i ≤ s and vi-1 ≠ vi+1 for 1 ≤ i ≤ s - 1. A graph Γ is called 2-transitive if it is (Aut(Γ), 2)-arc-transitive but not (Aut(Γ), 3)-arc-transitive. A Cayley graph Γ of a group G is called normal if G is normal in Aut(Γ) and nonnormal otherwise. Fang et al. ['On edge transitive Cayley graphs of valency four', European J. Combin. 25 (2004), 1103-1116] proved that if Γ is a tetravalent 2-transitive Cayley graph of a finite simple group G,..

View full abstract

University of Melbourne Researchers

Grants

Awarded by National Natural Science Foundation of China


Funding Acknowledgements

X. G. Fang and J. Wang were supported by the National Natural Science Foundation of China (Grant No. 11931005). S. Zhou was supported by the Research Grant Support Scheme of The University of Melbourne.