Eccentricity spectra of some graph operations in regular graphs

Abstract

The eccentricity matrix of a graph G is derived from its distance matrix by letting the ijᵗʰ entry be equal to the distance between two vertices i and j, if the distance is the minimum of their eccentricities and zero otherwise. The eigenvalues of the eccentricity matrix of G are called ε-eigenvalues. Its ε-spectrum is the set of εeigenvalues together with its multiplicity and ε-energy is the sum of the absolute values of the ε-eigenvalues. In this paper, we study the ε-spectra of certain operations on regular graphs. We also established some bounds on ε-energy of graphs and characterize the extreme graphs.