Spectra of eccentricity matrices of graphs

Abstract

The eccentricity matrix of a connected graph $G$ is obtained from the distance matrix of $G$ by retaining the largest distances in each row and each column, and setting the remaining entries as $0$. 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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References in corpus (1)

• Spectra of Coronae

Cited by in corpus (4)

• On the spectral radius and the energy of eccentricity matrix of a graph
• On the largest and least eigenvalues of eccentricity matrix of trees
• On the graphs having at most one positive eccentricity eigenvalue
• On graphs with exactly one anti-adjacency eigenvalue and beyond