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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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 Human and Digital Sciences > School of Computer Science and the Environment |
| Depositing User: | Atulya Nagar |
| Date Deposited: | 09 Jun 2016 11:11 |
| Last Modified: | 07 Mar 2025 11:57 |
| URI: | https://hira.hope.ac.uk/id/eprint/1070 |
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