Self-complementary distance-regular Cayley graphs over abelian groups

TL;DR

This paper investigates self-complementary distance-regular Cayley graphs over abelian groups, establishing their equivalence to self-complementary strongly regular graphs and providing specific examples over non-elementary abelian groups.

Contribution

It proves that self-complementary distance-regular graphs are necessarily self-complementary strongly regular graphs and constructs examples over non-elementary abelian groups.

Findings

Self-complementary distance-regular graphs are strongly regular.

Established the equivalence between self-complementary distance-regular and strongly regular Cayley graphs.

Provided explicit examples over non-elementary abelian groups.

Abstract

In this paper, we study self-complementary distance-regular Cayley graphs over abelian groups. We prove that if a regular graph is self-complementary distance-regular, then it is self-complementary strongly regular. We also deal with self-complementary strongly regular Cayley graphs over abelian groups and give an example of a self-complementary strongly regular Cayley graph over a non-elementary abelian group.