Recognizing bicoset digraphs which are $X$-joins and automorphism groups of bicoset digraphs

TL;DR

This paper studies the symmetry properties of bicoset digraphs, focusing on their automorphism groups and recognition methods for specific classes like $X$-joins, contributing to the understanding of their structural and automorphic characteristics.

Contribution

It introduces a method to determine automorphism groups of connected bicoset digraphs that are $X$-joins, based on their natural irreducible quotients and recognition from connection sets.

Findings

Automorphism groups can be derived from irreducible quotients.

Connected $X$-join bicoset digraphs can be recognized from their connection sets.

The paper characterizes symmetry properties of bicoset digraphs.

Abstract

We examine bicoset digraphs and their natural properties from the point of view of symmetry. We then consider connected bicoset digraphs that are $X$-joins with collections of empty graphs, and show that their automorphism groups can be obtained from their natural irreducible quotients. We then show that such digraphs can be recognized from their connection sets.