Table of Contents
International Journal of Computational Mathematics
Volume 2014, Article ID 436140, 8 pages
http://dx.doi.org/10.1155/2014/436140
Research Article

Modified Eccentric Connectivity of Generalized Thorn Graphs

1Department of Basic Sciences and Humanities (Mathematics), Calcutta Institute of Engineering and Management, Kolkata 700 040, India
2Department of Mathematics, National Institute of Technology, Durgapur 713 209, India
3Department of Mathematics, Aliah University, DN 20, Sector V, Salt Lake, Kolkata 700 091, India

Received 26 June 2014; Accepted 9 December 2014; Published 22 December 2014

Academic Editor: Sheung-Hung Poon

Copyright © 2014 Nilanjan De et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The thorn graph of a given graph is obtained by attaching pendent vertices to each vertex of . The pendent edges, called thorns of , can be treated as or , so that a thorn graph is generalized by replacing by and by and the respective generalizations are denoted by and . The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph in a hydrogen suppressed molecular structure. In this paper, we give the modified eccentric connectivity index and the concerned polynomial for the thorn graph and the generalized thorn graphs and .