On the distance spectra of graphs

2015/09/03 by Ghodratollah Aalipour, Aalipour, Ghodratollah, Aida Abiad +19 · 2 citations
Computer Science · Mathematics · #05C12 #05C31 #05C50 #15A15 #15A18 #15B48 #15B57 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1509.01196

openalex publication_date 2015/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The distance matrix of a graph G is the matrix containing the pairwise distances between vertices. The distance eigenvalues of G are the eigenvalues of its distance matrix and they form the distance spectrum of G. We determine the distance spectra of halved cubes, double odd graphs, and Doob graphs, completing the determination of distance spectra of distance regular graphs having exactly one positive distance eigenvalue. We characterize strongly regular graphs having more positive than negative distance eigenvalues. We give examples of graphs with few distinct distance eigenvalues but lacking regularity properties. We also determine the determinant and inertia of the distance matrices of lollipop and barbell graphs.

Citations

• On the diameter of Kneser graphs

Cited by

• The distance spectrum of the line graph of the crown graph
• When Are Standard Graph Products Isomorphic?

Related

• The generalized distance spectrum of a graph and applications
• Spectra of variants of distance matrices of graphs and digraphs: a survey
• Distance-regular graphs with a few q-distance eigenvalues
• Distance-regular graphs with exactly one positive q-distance eigenvalue
• On the Distance Spectra of Extended Double Stars