An infinite family of vertex-primitive 2-arc-transitive digraphs

TL;DR

This paper constructs an infinite family of vertex-primitive 2-arc-transitive digraphs, resolving a long-standing open problem in the field of algebraic graph theory.

Contribution

It introduces a novel construction method that proves the existence of infinitely many such digraphs, filling a major gap in the classification of symmetric digraphs.

Findings

Established the existence of infinitely many vertex-primitive 2-arc-transitive digraphs.

Provided explicit constructions for the new family of digraphs.

Resolved a long-standing open problem in algebraic graph theory.

Abstract

We solve the long-standing existence problem of vertex-primitive 2-arc-transitive digraphs by constructing an infinite family of such digraphs.