Energy and inertia of the eccentricity matrix of coalescence of graphs

Abstract

Graph energy is the sum of absolute values of the eigenvalues of the adjacency matrix of a graph. Eccentricity matrix, another graph matrix, was originally proposed, as DMAX matrix, by Randić (2013) [17] and redefined by Wang et al. (2018) [20], by using the concept of the eccentricities of vertices. In this paper, we study the irreducibility and the spectrum of the eccentricity matrix for particular classes of graphs, namely the windmill graphs, the coalescence of complete graphs and the coalescence of two cycles. We further estimate the eccentricity energy and inertia for the graphs of these classes. © 2021 Elsevier B.V.