Expected values of topological descriptors for possible kink chains of type ₂

In this paper, we investigate square-hexagonal chains, a class of systems where the inner dual of a structure with a square-hexagon shape forms a path graph. The specific configuration of square and hexagonal polygons, and how they are concatenated, leads to different types of square-hexagonal chains. A square containing a vertex of degree 2 is classified as having a kink, and the resulting kink is referred to as a type $$ kink. This kink is further subdivided into three types: $$ , ₂ $$ , and ₂ $$ . We focus on the kink chain of type ₂ $$ and compute various topological descriptors for this configuration. By deriving analytical expressions, we determine the maximizing and minimizing values of these descriptors. Additionally, we provide a comprehensive analysis of the expected values for these descriptors and offer a comparison of their behaviors through analytical, numerical, and graphical methods. These results offer insights into the structural properties and behavior of square-hexagonal chains, particularly in relation to the optimization of topological descriptors.