Cayley Incidence Graphs
Arnbj\"org Soff\'ia \'Arnad\'ottir, Alexey Gordeev, Sabrina Lato,, Tovohery Randrianarisoa, and Joannes Vermant

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.
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Taxonomy
TopicsAdvanced Graph Theory Research
