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.

A solitary number that can be utilized to describe some property of the graph of a particle is known as a topological index for that graph. There are various topological indices that have discovered a few applications in hypothetical science. In QSAR/QSPR think about, physico-concoction properties and topological indices, for example, Randic¢, atom-bond connectivity (ABC), geometric arithmetic (GA) and their edge renditions are utilized to anticipate the bioactivity of various substance mixes. In this paper, we consider the degree based molecular topological index the edge version of atom-bond connectivity index and geometric arithmetic index for line and line graph of subdivision of benzene ring embedded in P-type surface in 2D network. The diagnostic shut formulae for the edge version of atom-bond connectivity index and geometric arithmetic index of these classes of atomic structures are given

Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings ${\mathbb{Z}}_{p_1{p}_2}\times {\mathbb{Z}}_q$ , where $p_1,p_2$ , and q are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutative rings ${\mathbb{Z}}_{p_1{p}_2}\times {\mathbb{Z}}_q$ .

In this paper, we investigate the new graph characteristic, the edge irregularity strength, denoted as es, as a modification of the well known irregularity strength, total edge irregularity strength and total vertex irregularity strength. As a result, we obtain the exact value of an edge irregularity strength of corona product of cycle with isolated vertices

In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagreb polynomial is one of the degree based polynomials in a graph. A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, the first, second and third Zagreb polynomials of nanostar dendrimers are computed.