On graphs whose third largest distance eigenvalue dose not exceed −1

Jie Xue, Ruifang Liu and Jinlong Shu

Applied Mathematics and Computation, 2021, vol. 402, issue C

Abstract: In this paper, the distance eigenvalues of chain graphs are discussed. Using clique extension, we characterize all connected graphs whose third largest distance eigenvalue is at most −1. As an application, it is proved that a graph is determined by its distance spectrum if its third largest distance eigenvalue is less than −1.

Keywords: Third largest eigenvalue; Distance matrix; Distance spectra; Chain graph (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300321001855

DOI: 10.1016/j.amc.2021.126137

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