Nagar, Atulya and Sastha, Sriram (2016) On Eccentric Connectivity Index of Eccentric Graph of Regular Dendrimer. Mathematics in Computer Science. ISSN 16618270

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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/s117860160259z." 
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:  16 Oct 2017 19:13 
URI:  http://hira.hope.ac.uk/id/eprint/1070 
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