An infinite family of cubic nonnormal Cayley graphs on nonabelian simple groups

TL;DR

This paper constructs an infinite family of connected cubic nonnormal Cayley graphs on nonabelian simple groups, specifically on alternating groups of order 2^m - 1, and determines their automorphism groups.

Contribution

It introduces the first known infinite family of connected cubic nonnormal Cayley graphs on nonabelian simple groups, expanding understanding of Cayley graph structures.

Findings

Constructed a connected cubic nonnormal Cayley graph on A_{2^m-1} for m ≥ 4

Determined the full automorphism group of these graphs

Established this as the first infinite family of such graphs on nonabelian simple groups

Abstract

We construct a connected cubic nonnormal Cayley graph on $\mathrm{A}_{2^m-1}$ for each integer $m\geqslant4$ and determine its full automorphism group. This is the first infinite family of connected cubic nonnormal Cayley graphs on nonabelian simple groups.