On cubic graphical regular representations of finite simple groups

TL;DR

This paper advances the understanding of cubic graphical regular representations by proving that all large-rank finite simple groups of Lie type possess such representations, supporting a conjecture about their finiteness.

Contribution

It provides a significant proof that large-rank finite simple groups of Lie type have cubic graphical regular representations, confirming part of a broader conjecture.

Findings

Large-rank finite simple groups of Lie type have cubic graphical regular representations.

Supports the conjecture that only finitely many finite simple groups lack such representations.

Abstract

A recent conjecture of the author and Teng Fang states that there are only finitely many finite simple groups with no cubic graphical regular representation. In this paper, we make a crucial progress towards this conjecture by giving an affirmative answer for groups of Lie type of large rank.