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arXiv · 1902.02608

Spectra of eccentricity matrices of graphs

Iswar Mahato·R. Gurusamy·M. Rajesh Kannan·S. Arockiaraj
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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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Iswar Mahato, R. Gurusamy, M. Rajesh Kannan, S. Arockiaraj. 2019-02-07. Spectra of eccentricity matrices of graphs. https://doi.org/10.1016/j.dam.2020.05.029

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