On Eccentric Connectivity Index of Eccentric Graph of Regular Dendrimer

The eccentric connectivity index
of a connected graph G is defined as
where deg(v) is the degree of vertex v and e(v) is the eccentricity of v. The eccentric graph,
, of a graph G has the same set of vertices as G, with two vertices u, v adjacent in
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.