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

作者：

Highlights：

• In thispaper,the distance eigenvalues of chain graphs are originally discussed. We present the chain graphs whose third largest distance eigenvalues are atmost-1.

• Furthermore, using clique extension, we characterize all connected graphs whose third largest distance eigenvalue is atmost-1.

• As an application, it is proved that a graph is determined by its distance spectrum if its third largest distance eigenvalue is lessthan-1. This is our important goal and highlight.

摘要

•In thispaper,the distance eigenvalues of chain graphs are originally discussed. We present the chain graphs whose third largest distance eigenvalues are atmost-1.•Furthermore, using clique extension, we characterize all connected graphs whose third largest distance eigenvalue is atmost-1.•As an application, it is proved that a graph is determined by its distance spectrum if its third largest distance eigenvalue is lessthan-1. This is our important goal and highlight.

论文关键词：Third largest eigenvalue,Distance matrix,Distance spectra,Chain graph

论文评审过程：Received 20 October 2020, Revised 13 February 2021, Accepted 24 February 2021, Available online 6 March 2021, Version of Record 6 March 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126137