On Eccentric Connectivity Index of Eccentric Graph of Regular Dendrimer

Nagar, Atulya and Sastha, Sriram (2016) On Eccentric Connectivity Index of Eccentric Graph of Regular Dendrimer. Mathematics in Computer Science. ISSN 1661-8270

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Official URL: http://link.springer.com/article/10.1007/s11786-01...

Abstract

The eccentric connectivity index \(\xi ^c(G)\) of a connected graph G is defined as \(\xi ^c(G) =\sum _{v \in V(G)}{deg(v) e(v)},\) where deg( v) is the degree of vertex v and e( v) is the eccentricity of v. The eccentric graph, \(G_e\), of a graph G has the same set of vertices as G; with two vertices u; v adjacent in Ge if and only if either u is an eccentric vertex of v or v is an eccentric vertex of u: In this paper, we obtain a formula for the eccentric connectivity index of the eccentric graph of a regular dendrimer. We also derive a formula for the eccentric connectivity index for the second iteration of eccentric graph of regular dendrimer.

Item Type: Article
Additional Information and Comments: “The final publication is available at http://link.springer.com/article/10.1007/s11786-016-0259-z."
Keywords: Dendrimer · Eccentricity · Eccentric graph · Eccentric connectivity index
Faculty / Department: Faculty of Science > Mathematics and Computer Science
Depositing User: Atulya Nagar
Date Deposited: 09 Jun 2016 11:11
Last Modified: 23 Mar 2017 01:15
URI: http://hira.hope.ac.uk/id/eprint/1070

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