Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.

In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph $G=(V,E)$ , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a capacity characterized defined is known as a vertex-marked graph. Similarly, an edge naming is a mapping of an element of E to an arrangement of marks. In this case, the diagram is called an edge-marked graph. We consider an edge irregular reflexive k-labeling for the disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the disjoint association of m copies of some wheel-related graphs, specifically gear graphs and prism graphs.

The optical transpose interconnection system (OTIS) network has many application in architecture for parallel as well as in distributed network. The optical translate interconnection system utilizes a straightforward pair of lenslet clusters to execute a coordinated interconnection that is valuable for mix based multistage interconnection networks, work of-trees network processors, and hypercubes. In Cancan (2019) and Hayat et al. (2014), different interconnection network has studied related to topological indices. In this article we have computed the Ve-degree and Ev-degree base topological indices of swapped network by taking path and complete graph as original graphs. We have included some dedicated formulas for different types of topological indices for the OTIS swapped network by taking the path and complete graph on $n$ vertices as basis of graph.

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.

Topological indices play a very important role in the study of structure of a chemical graph. There are many types of topological indices which describe quantitative properties of the structure of different graphs and molecular networks of chemical graphs. In the beginning of the study of topological indices, there were three different types of indices which were based on degree, distance and counting. M. Chellali et al. (“On Ve-Degrees and Ev-Degrees in Graphs,” Discrete Mathematics 340, no. 2 (2017): 31–8) introduced V_e- degree and E_v- degree based topological indices. This article is a contribution to the study of V_e-degree and E_v-degree based topological indices for series of concealed non-Kekulean benzenoid graph. In this article, we have calculated ten different types of topological indices which are based on V_e-degree and E_v-degree for the series of concealed non-Kekulean benzenoid graph.

Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and radio labeling. Secrecy of data in data sciences and in information technology is very necessary as well as the accuracy of data transmission and different channel assignments is maintained. It enhances the graph terminologies for the computer programs. In this paper, we will discuss multidistance radio labeling used for channel assignment problems over wireless communication. A radio labeling is a one-to-one mapping satisfying the condition for any pair of vertices in . The span of labeling is the largest number that assigns to a vertex of a graph. Radio number of , denoted by , is the minimum span taken over all radio labelings of . In this article, we will find relations for radio number and radio mean number of a lexicographic product for certain families of graphs.