The eccentricity extended energy of a graph

B. Sharada; A. M. Naji; Mohammad Issa Sowaity

doi:10.17777/pjms.2019.22.2.011

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The eccentricity extended energy of a graph

B. Sharada|A. M. Naji|Mohammad Issa Sowaity

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Eccentricity of a vertex eccentricity extended matrix eccentricity extended eigenvalues eccentricity extended energy of a graph

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Let ei be the eccentricity of the vertex vi of a graph G, where ei = maxfd(u; v) : u 2 V (G)g. In this paper, we introduce the eccentricity extended matrix Aeex(G), so that its (i,j)-entry is equal to 1 2 ( ei ej + ej ei ) for vivj 2 E and 0 otherwise. Some properties of the eccentricity extended spectral radius 1 are obtained. The eccentricity extended energy Eeex(G) of G is dened. Uper and lower bounds for Eeex(G) are established.

Abstract

Let ei be the eccentricity of the vertex vi of a graph G, where ei = maxfd(u; v) : u 2 V (G)g. In this paper, we introduce the eccentricity extended matrix Aeex(G), so that its (i,j)-entry is equal to 1 2 ( ei ej + ej ei ) for vivj 2 E and 0 otherwise. Some properties of the eccentricity extended spectral radius 1 are obtained. The eccentricity extended energy Eeex(G) of G is dened. Uper and lower bounds for Eeex(G) are established.

참고문헌 (21)

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