Mohamad Nazri Husin

On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations

Let dL(G)(e) be the degree of an edge e in line graph L(G) of a graph G. The edge versions of atom-bond connectivity (ABCe) and geometric arithmetic (GAe) indices of G are defined as efE(L(G))(dL(G)(e)+dL(G)(f)2dL(G)(e)dL(G)(f) and GAe(G)=efE(L(G))2dL(G)(e)dL(G)(f)dL(G)(e)+dL(G)(f). In this paper, we study the ABCe and GAe indices for joint graphs and certain graph operations.

On Topological Indices of Certain Families of Nanostar Dendrimers

A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

More results on computation of topological indices of certain networks

There are certain types of topological indices such as degree-based topological indices, distance-based topological indices and counting-related topological indices. Among degree-based topological indices, the so-called atom-bond connectivity (ABC), geometric-arithmetic (GA) are of vital importance. These topological indices correlate certain physico-chemical properties of chemical compounds such as boiling point, stability, strain energy and others. In this paper, the augmented Zagreb, first reformulated Zagreb and sum connectivity indices for certain networks like silicate, chain silicate, hexagonal, oxide and honeycomb networks are computed.

Atom-bond connectivity index of graph with three edges added

The atom-bond connectivity index of a graph G, denoted as ABC(G), is the most important topological indices in chemical graph theory. The ABC index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes. In this note, we prove that the ABC index of a graph increases when three new edges are added.