Multiplicative Attributes Derived from Graph Invariants for Saztec4 Diamond

Abstract

This study consists of developing some closed and updated formulas derived from multiplicative graph invariants such as general Randic index $\left(\text{GRI}\right)R_{{\lambda }^0}\left(\varkappa \right)$ for ${\lambda }^0=\left\{\pm 1\text{,}\pm 1/2\right\}$ , ordinary general geometric-arithmetic (OGA), general version of harmonic index (GHI), sum connectivity index (SI), general sum connectivity index (GSI), 1st and 2nd Gourava and hyper-Gourava indices, (ABC) index, Shegehalli and Kanabur indices, 1st generalised version of Zagreb index (GZI), and forgotten index (FI) for the subdivided Aztec diamond network. Aztec diamond is constructed based on the squares boxes. These square boxes are placed at the centre point and nourish the condition $\left|s-\left(1/2\right)\right|+\left|r-\left(1/2\right)\right|\le n$ . Furthermore, we put a new vertex of degree-2 at each edge of the small boxes, squares in shapes. A new structure is obtained that has the same properties as its parental graph and is called a subdivided Aztec diamond and symbolised as Saztecn. Subsequently, we compute the multiplicative topological attributes to get some new formulas. For this purpose, a simple, connected, and the finite graph is considered by supposing it Y as the graph of the Saztecn. The order and size have also been discussed in this study and found three different kinds of edges (2, 2), (2, 3), and (2, 4) for computing. The discussion on the networks mentioned above provides us with essential results that can be used in the determination of bio and physio activities and can be interspersed with the molecular compounds and their graphical structures better to understand their physical as well as biological properties.