Oriented regular representations of out-valency two for finite simple groups

TL;DR

This paper proves that all finite simple groups of order at least 5 can be represented with an oriented regular graph of out-valency 2, expanding understanding of their symmetrical properties.

Contribution

It establishes that every finite simple group of order at least 5 admits an oriented regular representation with out-valency 2, a new result in group and graph theory.

Findings

Finite simple groups of order ≥ 5 admit oriented regular representations of out-valency 2.

The result applies to all such groups, regardless of their specific structure.

This advances the classification of symmetries in finite simple groups.

Abstract

In this paper, we show that every finite simple group of order at least $5$ admits an oriented regular representation of out-valency $2$.