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.

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.

This paper deals with decomposition of complete graphs on n vertices into circulant graphs with reduced degree r < n-1. They are denoted as Cn(a1, a2,..., am), where a1 to am are generators. Mathematical labeling for such bigger (higher order and huge size) and complex (strictly regular with so many triangles) graphs is very difficult. That is why after decomposition an edge irregular k-labeling for these subgraphs is computed with the help of algorithmic approach. Results of k are computed by implementing this iterative algorithm in computer. Using the values of k an upper bound for edge irregularity strength is suggested for Cn(a1, a2,..., am) that is |E|/2 log2 |V|.

In recent past 2D metal trihalides have evolved as useful gapless semiconductor due to their physical properties like low dimensional magnetism and thermo electric performance. Such highly appreciable physical properties of these material are because enormous natural properties like half-metallicity, polarization, spin-orbit coupling impacts, layered structure and low cost. Layered formation of these materials provides an opportunity for the field of mathematical chemistry for identification of patterns and computation of mathematical properties. This article is dedicated to compute vertex-edge-degree based topological characterization of 2D trihalides. General mathematical expressions of several vertex-edge-degree based topological indices are presented in terms of research outcomes so they can be effectively used in future industrial projects.

Let G = (V;E) be a graph. A total labeling ψ : V ⋃ E → {1, 2, ....k} is called totally irregular total k-labeling of G if every two distinct vertices u and v in V (G) satisfy wt(u) ≠wt(v); and every two distinct edges u1u2 and v1v2 in E(G) satisfy wt(u1u2) ≠ wt(v1v2); where wt(u) = ψ (u) + ∑uv∊E(G) ψ(uv) and wt(u1u2) = ψ(u1) + ψ(u1u2) + ψ(u2): The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G): In this paper, we determine the exact value of the total irregularity strength of cubic graphs.

Consider λ to be a connected graph with a vertex set V(λ) that may be partitioned into any partition set S. If each vertex in λ has a separate representation with regard to S and is an ordered k partition, then the set with S is a resolving partition of λ.. A partition dimension of λ, represented by pd, is the minimal cardinality of resolving k partitions of V(λ). The partition dimension of various generalised families of graphs, such as the Harary graph, Cayley graph, and Pendent graph, is given as a sharp upper bound in this article.