Divisible design Cayley digraphs

TL;DR

This paper studies divisible design digraphs that are Cayley digraphs, providing characterizations, constructions, and a classification for graphs with up to 27 vertices.

Contribution

It offers a characterization of divisible design Cayley digraphs based on generating sets and classifies such digraphs up to 27 vertices.

Findings

Characterization of divisible design Cayley digraphs in terms of generating sets

Several new constructions of divisible design Cayley digraphs

Classification of these digraphs for up to 27 vertices

Abstract

Divisible design digraphs which can be obtained as Cayley digraphs are studied. A characterization of divisible design Cayley digraphs in terms of the generating sets is given. Further, we give several constructions of divisible design Cayley digraphs and classify divisible design Cayley digraphs on $v \le 27$ vertices.