Exploring structural variations and topological descriptors of square-hexagonal kink chains of type T 2,2 in engineering applications

Square-hexagonal kink chains, also known as hexagonal kink chains or simply kink chains, are structural configurations used in engineering for various purposes, including material science, nano-technology and mechanics. The square hexagonal kink chain likely describes a chain-like structure where the individual units have square and hexagon-like shapes and are arranged with symmetry. Additionally, there are likely points in the chain where the linear arrangement deviates or kinks, possibly due to some structural irregularity. A nonterminal hexagon is regarded as a kink if it contains two neighbouring vertices of degree [Formula: see text], while a nonterminal square is considered a kink if and only if it has a vertex of degree [Formula: see text]. The kinks from these two types of arrangements are called kinks of type [Formula: see text] and [Formula: see text], respectively. Our objective is to discover three possible arrangements of kinks of type [Formula: see text] further, depending on the process of how different polygons are attached at different places, holding the condition to make a kink at each step. In this work, we have calculated forgotten, geometric-arithmetic, sum-connectivity and atom bond-connectivity indices for the kink chains. A comparison between these topological descriptor is given by computing their numerical values for each kink chain.