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)"

Fifth Geometric-Arithmetic Index of Polyhex Zigzag TUZC6[m,n] Nanotube and Nanotori

Among topological descriptors, connectivity indices are very important and they have a prominent role in chemistry. The geometric-arithmetic index (GA) index is a topological index was defined as GA (G) in which degree of a vertex v denoted by dv. A new version of GA index was defined by A. Graovac et al recently, and is equale to GA (G) where GA (G) In this paper, we compute this new topological connectivity index for polyhex zigzag TUZC6[m,n] Nanotube and Nanotori

Computing the Omega polynomial of an infinite family of the linear parallelogram P(n,m)

Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges. The Omega polynomial Ω(G,x) was introduced by Diudea in 2006 and this defined as  where m(G,c) the number of qoc strips of length c. In this paper, we compute the omega polynomial of an infinite family of the linear parallelogram P(n,n) of benzenoid graph

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

Modified Eccentric Connectivity Polynomial of Circumcoronene Series of Benzenoid Hk

Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices/atoms and E(G) is a set of edges/bonds. For vV(G), defined dv be degree of vertex/atom v and S(v)is the sum of the degrees of its neighborhoods. The modified eccentricity connectivity polynomial of a molecular graph G is defined as  where ε(v) is defined as the length of a maximal path connecting v to another vertex of molecular graph G. In this paper we compute this polynomial for a famous molecular graph of Benzenoid family

Fourth Atom-Bond Connectivity Index of an Infinite Class of Nanostar Dendrimer D3[n]

The atom-bond connectivity (ABC) index of a graph G is a connectivity topological index was defined as  where dv denotes the degree of vertex v of G. In 2010, M. Ghorbani et. al. introduced a new version of atom-bond connectivity index as  where  In this paper, we compute a cloused formula of ABC4 index of an infinite class of Nanostar Dendrimer D3[n]. A Dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers

Computing a Counting Polynomial of an Infinite Family of Linear Polycene Parallelogram Benzenoid Graph P(a,b)

Omega polynomial was defined by M.V. Diudea in 2006 as  where the number of edges co-distant with e is denoted by n(e). One can obtain Theta Θ, Sadhana Sd and Pi Π polynomials by replacing xn(e) with n(e)xn(e), x|E|-n(e) and n(e)x|E|-n(e) in Omega polynomial, respectively. Then Theta Θ, Sadhana Sd and Pi Π indices will be the first derivative of Θ(x), Sd(x) and Π(x) evaluated at x=1. In this paper, Pi Π(G,x) polynomial and Pi Π(G) index of an infinite family of linear polycene parallelogram benzenoid graph P(a,b) are computed for the first time

The Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk

The omega polynomial Ω(G,x), for counting qoc strips in molecular graph G was defined by Diudea as  with m(G,c), being the number of qoc strips of length c. The Theta polynomial Θ(G,x) and the Theta index Θ(G) of a molecular graph G were defined as Θ(G,x)= and Θ(G)=, respectively.In this paper, we compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk, for all positive integer number k.Â

Connective Eccentric Index of Circumcoronene Homologous Series of Benzenoid H k

ABSTRACT Let G be a molecular graph, a topological index is a numeric quantity related to G which is invariant under graph automorphisms. The eccentric connectivity inde