ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS

ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS

S. Surya, P. Ramachandran

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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 ε- eigenvalues 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.

Keywords

eccentricity matrix, distance matrix, spectrum, energy, eigenvalue.