New constructions of divisible design Cayley graphs

TL;DR

This paper introduces new methods for constructing divisible design Cayley graphs and provides a classification for such graphs with up to 27 vertices, advancing understanding in algebraic graph theory.

Contribution

It presents novel constructions of divisible design Cayley graphs and classifies all such graphs with up to 27 vertices, expanding the known catalog.

Findings

New constructions of divisible design Cayley graphs

Complete classification for graphs with v ≤ 27 vertices

Enhanced understanding of algebraic properties of these graphs

Abstract

Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. Further, divisible design graphs which can be obtained as Cayley graphs were recently studied by Kabanov and Shalaginov. In this paper we give new constructions of divisible design Cayley graphs and classify divisible design Cayley graphs on $v \le 27$ vertices.