Abdul Jalil Manshad Khalaf Khalaf

In this paper, we compute the Atom Bond Connectivity Index for certain vertex gluing

In this paper, we study the Connectivity Index of Molecular Graphs of Chemical Trees with Application to Alkynes

In this paper, we study the Atom Bond Connectivity Index of Molecular Graphs of Alkynes and Cycloalkynes.

For a commutative ring R, the zero-divisor graph of R is the graph whose vertices are the nonzero zero-divisors of R such that the vertices x and y are adjacent if and only if Let denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written if A graph G is chromatically unique written c-unique, if for any graph H, implies that G is isomorphic with H. This paper focuses on the chromatic polynomials, the chromatic equivalence and the chromatic uniqueness of certain types of zero-divisor graphs.

The atom-bond connectivity (ABC) index is one of the newly most studied degree based molecular structure descriptors, which have chemical applications. For a graph G, the ABC index can be defined as ABC (G)= Σ uv∈ E (G) dv+ du− 2/dv. du, where du, the degree of the vertex u is the number of edges with u as an end vertex denotes the degree of a vertex u in G. In this paper, we establish the general formulas for the atom bond connectivity index of molecular graphs of alkenes and cycloalkenes.

Let G=(V, E) be a simple connected molecular graph. In such a simple molecular graph, vertices and edges are depicted atoms and chemical bonds respectively, we refer to the sets of vertices by V (G) and edges by E (G). If d (u, v) be distance between two vertices u, v∈ V (G) and can be defined as the length of a shortest path joining them. Then, the eccentricity connectivity index (ECI) of a molecular graph G is ξ (G)=∑ v∈ V (G) d (v) ec (v), where d (v) is degree of a vertex v∈ V (G). ec (v) is the length of a greatest path linking to another vertex of v. In this study, we focus the general formula for the eccentricity connectivity index (ECI) of some chemical trees as alkenes.

The distinguishing number (index) of a graph G is the least integer d such that G has a vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. In this paper, we compute the distinguishing number and the distinguishing index for the join of two specific graphs.

In this paper, we study the eccentric connectivity index of certain graphs.

The atom bond connectivity (ABC) index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes, which is defined as ABC = uv∈E(G) du+dv −2 dudv , we denotes du the degree of vertex u in G. In this paper, we study the general formula for ABC index of certain graphs and vertex gluing of graphs.

Let G = (V, E) be a simple connected molecular graph. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V(G) and E(G), respectively. If d(u, v) be the notation of distance between vertices u, v ε V(G) and is defined as the length of a shortest path connecting them. Then, the eccentricity connectivity index of a molecular graph G is defined as ζ(G) = Σ vεv(G) deg(v)ec(v), where deg(v) is degree of a vertex v ε V(G), and is defined as the number of adjacent vertices with v. ec(v) is eccentricity of a vertex v ε V(G), and is defined as the length of a maximal path connecting to another vertex of v. In this paper, we establish the general formulas for the eccentricity connectivity index of some classes of chemical trees.