Nabeel E. Arif

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.

Fourth order connectivity index of polyphenylene dendrimers

A simple graph G = (V,E) is a finite nonempty set V(G) of objects called vertices together with a (possibly empty) set E(G) of unordered pairs of distinct vertices of G called edges. In chemical graphs, the vertices of the graph correspond to the atoms of the molecule, and the edges represent the chemical bonds. Dendrimers are hyper-branched macromolecules, with a rigorously tailored architecture. They can be synthesized, in a controlled manner, either by a divergent or a convergent procedure. Their applications in chemistry, biology and nano-science are unlimited. A single number which characterizes the graph of a molecular is called a graph theoretical invariant or topological index. The connectivity index is one of the most popular molecular-graph. Recently, some researchers investigated m-order connectivity indices of some dendrimer nanostars, where m = 2 and 3. In this paper, the 4-order connectivity index of an infinite family of polyphenylene dendrimers is investigated.