Abstract

Let G be an undirected, finite and simple graph with m points and n lines. For any integer 1$\leq$ k $<$$\infty$, generalized eccentricity k$^{th}$ power product matrix of G is a m$\times$m matrix with (r,s)$^{th}$ entry as (e$_{r}$$^{k}$ . e$_{s}$$^{k}$) if r is not equal to s and zero or else, where e$_{r}$ is the eccentricity of the r$^{th}$ vertex of G. In this paper, the new energy of graph under the name as generalized eccentricity k$^{th}$ power product energy of a graph G (EGE$^{k}$P(G)) has been introduced. Also we obtain bounds for the generalized eccentricity k$^{th}$ power product eigenvalues and generalized eccentricity k$^{th}$ power sum energy of a graph G (EGE$^{k}$P(G)). GE$^{k}$P(G) energies of some standard graphs have been attained.

Keywords and Phrases

Eccentricity, generalized eccentricity k$^{th}$ power product matrix, generalized eccentricity k$^{th}$ power product polynomial, eigenvalues and generalized eccentricity k$^{th}$ power product energy.

A.M.S. subject classification

05C50.

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