Computing Atom-Bond Connectivity (ABC4) index for Circumcoronene Series of Benzenoid

Let G=(V; E) be a simple connected graph. The sets of vertices and edges of G are denoted by V=V(G) and E=E (G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The Atom-Bond Connectivity (ABC) index is a topological index was defined as  where dv denotes degree of vertex v. In 2010, a new version of Atom-Bond Connectivity (ABC4) index was defined by M. Ghorbani et. al as  where and NG(u)={vV(G)|uvE(G)}. The goal of this paper is to compute the ABC4 index for Circumcoronene Series of Benzenoi

Computing Fifth Geometric-Arithmetic Index for Circumcoronene series of benzenoid Hk

Let G=(V; E) be a simple connected graph. The sets of vertices and edges of G are denoted by V=V(G) and E=E (G), respectively. The geometric-arithmetic index is a topological index was introduced by Vukicevic and Furtula in 2009 and defined as  in which degree of vertex u denoted by dG(u) (or du for short). In 2011, A. Graovac et al defined a new version of GA index as  where  The goal of this paper is to compute the fifth geometric-arithmetic index for "Circumcoronene series of benzenoid Hk (k≥1)"