The Degree-Based Topological Indices for Two Special Families of Graphs of Diameter Three

Abstract

In this research article, we determine some vertex degree-based topological indices or descriptors of two families of graphs, i.e., $G=C_4\left(K_n\right)$ and $G=C_4\left(K_n\right)+v_1{v}_3$ , where $C_4\left(K_n\right)$ is a graph obtained by identifying one of the vertices of $K_n$ with one vertex of $C_4$ . Similarly, a graph formed by joining one of the vertices of $K_n$ with one vertex of $C_4+v_1{v}_3$ is known as the $C_4\left(K_n\right)+v_1{v}_3$ graph.