Spectra of eccentricity matrices of graphs
arXiv:1902.02608 · doi:10.1016/j.dam.2020.05.029
Abstract
The eccentricity matrix of a connected graph is obtained from the distance matrix of by retaining the largest distances in each row and each column, and setting the remaining entries as . In this article, a conjecture about the least eigenvalue of eccentricity matrices of trees, presented in the article [Jianfeng Wang, Mei Lu, Francesco Belardo, Milan Randic. The anti-adjacency matrix of a graph: Eccentricity matrix. Discrete Applied Mathematics, 251: 299-309, 2018.], is solved affirmatively. In addition to this, the spectra and the inertia of eccentricity matrices of various classes of graphs are investigated.
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