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In this research article, we determine some vertex degree-based topological indices or descriptors of two families of graphs, i.e.,  G = C 4 K n and  G = C 4 K n + v 1 v 3 , where  C 4 K n 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 K n + v 1 v 3 graph.

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