On the distance eigenvalues of design graphs

TL;DR

This paper investigates the distance eigenvalues of design graphs, a special class of bipartite graphs related to strongly regular graphs, and identifies conditions for their eigenvalues to be integers.

Contribution

It explicitly determines the distance eigenvalues of certain design graphs and characterizes when these graphs are distance integral.

Findings

Explicit formulas for distance eigenvalues of a class of design graphs

Conditions for design graphs to be distance integral

Enhanced understanding of spectral properties of design graphs

Abstract

A design graph is a regular bipartite graph in which any two distinct vertices of the same part have the same number of common neighbors. This class of graphs have a close relationship to strongly regular graphs. In this paper, we study the distance eigenvalues of the design graphs. Also, we will explicitly determine the distance eigenvalues of a class of design graphs, and determine the values for which the class is distance integral, that is, its distance eigenvalues are integers.