On the distance eigenvalues of design graphs

2021/11/09 by Mirafzal, S. Morteza · 2 citations
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.05239

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.

Cited by

• The distance spectrum of the bipartite double cover of strongly regular graphs
• The distance spectrum of the line graph of the crown graph

Related

• The distance-regular graphs such that all of its second largest local eigenvalues are at most one
• The line graph of the crown graph is distance integral
• On the distance spectra of graphs
• Distance-regular graphs with valency k having smallest eigenvalue at most -k/2
• The distance spectrum of the line graph of the crown graph