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

Text
dendrimer.pdf Download (106kB)  Preview 
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:  23 Mar 2017 01:15 
URI:  http://hira.hope.ac.uk/id/eprint/1070 
Actions (login required)
View Item 