The second eccentric Zagreb index of the n^{th} growth nanostar dendrimer D_{۳}[n]

Let G=(V,E) be an ordered pair, where V(G) is a non-empty setof vertices and E(G) is a set of edges called a graph. We denotea vertex by v where v \in V(G) and edge by e where e=uv \inE(G). we denote degree of vertex v by d_{v} which is definedas the number of edges adjacent with vertex v. The distancebetween two vertices of G is the length of a shortest pathconnecting these two vertices which is denoted by d(u,v) whereu,v \in V(G). The eccentricity ecc(v) of a vertex v in Gis the distance between vertex v and vertex farthest from v inG. In this paper, we consider an infinite family of NanostarDendrimers and compute its Second Eccentric Zagreb index.M.Ghorbani and Hosseinzadeh introduced Second eccentric zagrebindex as EM_{۲}(G)=\sum_{uv \in E(G)}\big(ecc(u)\timesecc(v)\big), that ecc(u) denotes the eccentricity of a vertexu and ecc(v) denotes the eccentricity of a vertex v of G.

Keywords:

Eccentricity , Zagreb topological index , nanostar dendrimer , D_{۳}[n]