On the distance spectra of graphs

G. Aalipour,, Aida Abiad Monge, L. Hogben, Z. Berikkyzy, J. Cummings, J. De Silva, W. Gaok, K. Heysse, J.C.-H. Lin, M. Tait, F.H.J. Kenter

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)

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 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.
Original languageEnglish
Pages (from-to)66-87
JournalLinear Algebra and Its Applications
Volume497
Issue number15 May 2016
DOIs
Publication statusPublished - 2016
Externally publishedYes

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