Cayley Incidence Graphs

TL;DR

This paper explores Cayley incidence graphs, a biregular extension of Cayley graphs, and investigates their properties and connections to hypergraphs, geometries, and combinatorial structures.

Contribution

It reformulates the definition of Cayley incidence graphs and establishes their relationships with hypergraphs, coset geometries, difference sets, and cages.

Findings

Reformulation of Cayley incidence graphs

Connections to Cayley hypergraphs and geometries

Basic properties of these graphs

Abstract

Evra, Feigon, Maurischat, and Parzanchevski (2023) introduced a biregular extension of Cayley graphs. In this paper, we reformulate their definition and provide some basic properties. We also show how these Cayley incidence graphs relate to various notions of Cayley hypergraphs. We further establish connections between Cayley incidence graphs and certain geometric and combinatorial structures, including coset geometries, difference sets and cages.