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 ${\mathbb{Z}}_{p_1{p}_2}\times {\mathbb{Z}}_q$ .

The Optical Transpose Interconnection System (OTIS) has applications in parallel processing, distributed processing, routing, and networks. It is used for efficient usage of multiple parallel algorithms or parallel systems, with different global interconnections in a network as it is an optoelectronic (combination of light signals and electronics). In chemical graph theory, topological indices are used to study characteristics of the chemical structures or biological activities. Topological indices are sometimes studied with the assistance to their polynomial. In this article, polynomials of degree-based topological indices for OTIS and swapped networks have been studied. Results can be used to compute any degreebased topological polynomials for OTIS swapped network.

The transition metal is a planar metallic organic structure, and tetra-cyano-benzene is one of the most studied networks of 3d series of transition metal. Tetra-cyano-benzene behaved as a useful object in the alloy synthesis industry due to its excellency of hardness. In spintronics, the tetra-cyano-benzene demonstrate a long-range ferromagnetic connection in the erection of magnetic, which is usually behaved as the ideal entrant. To study this novel tetra-cyano-benzene structure, we use an authentic mathematical tool known as M-polynomials of the topological index and shows some physical and chemical properties in numerical form, to understand the structure deeply we compare different legitimate M-polynomials of topological indices and concluding in the form of figurative comparisons.

Metal organic structures and networks are extensively studied in modern chemistry. These networks are extremely adaptable and useful in a variety of fields. Metal organic networks are thought to be the home of gases, and this structure is also engaged in gas purification and separation. The fact that they have so much utility and applicability stems from that they have so many distinct properties, such as exchanging ions and altering organic ligands. This structure’s chemical and physical properties are considered. There are extensive, time‐consuming, and costly experiments available to investigate these physical and chemical properties. To avoid these complex experiments and tests, a mathematical study provides approximate details of these chemical and physical behaviors of a structure, which is known as topological descriptors. In this work, we discussed the metal organic network’s line graph and studied the structural properties of the resulted network with the help of topological descriptors.

Natural zeolites are commonly described as macromolecular sieves. Zeolite networks are very trendy chemical networks due to their low-cost implementation. Sodalite network is one of the most studied types of zeolite networks. It helps in the removal of greenhouse gases. To study this rich network, we use an authentic mathematical tool known as M-polynomials of the topological index and show some physical and chemical properties in numerical form, and to understand the structure deeply, we compare different legitimate M-polynomials of topological indices, concluding in the form of graphical comparisons.