A construction of 2-arc-transitive non-solvable covers of complete graphs

TL;DR

This paper constructs specific 2-arc-transitive covers of complete graphs with non-abelian simple groups, addressing an open problem in graph symmetry and group actions.

Contribution

It provides the first known construction of non-solvable 2-arc-transitive covers of complete graphs, solving an important existence question.

Findings

Constructed connected 2-arc-transitive covers with non-abelian simple groups.

Solved the existence problem for non-solvable 2-arc-transitive covers.

Advances understanding of symmetry in graph covers.

Abstract

We construct connected $2$-arc-transitive covers of complete graphs with non-abelian characteristically simple transformation groups. This solves the existence problem for non-solvable $2$-arc-transitive covers of complete graphs.