Eccentric Connectivity Index: Extremal Graphs and Values

Document Type : Research Paper


1 University of Zagreb, CROATIA

2 University of Kashan, I. R. IRAN

3 University of Split , CROATIA


Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine the leading coefficient in the asymptotic behavior.