The second eccentric Zagreb index of the N^TH growth nanostar dendrimer D3[N]

Let g = (v,e) be an ordered pair, where v(g) is a non-empty set of vertices and e(g) is a set of edges called a graph. we denote a vertex by v, where v ∈ v(g) and edge by e, where e = uv ∈ e(g). we denote degree of vertex v by dv which is defined as the number of edges adjacent with vertex v. the distance between two vertices of g is the length of a shortest path connecting these two vertices which is denoted by d(u,v) where u,v ∈ v(g). the eccentricity ecc(v) of a vertex v in g is the distance between vertex v and vertex farthest from v in g. in this paper, we consider an infinite family of nanostar dendrimers and then we compute its second eccentric zagreb index. ghorbani and hosseinzadeh introduced the second eccentric zagreb index as em2(g) = σ_uv∈e(g) (ecc(u) × ecc(v)), that ecc(u) denotes the eccentricity of vertex u and ecc(v) denotes the eccentricity of vertex v of g.