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 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.
Highlights
Around the center of a century ago, theoretical experts found some interesting relationships between different properties of organic substances and those of molecular structure by analyzing a few invariants of the underlying molecular graph
These graph invariants are useful for molecular objects and are named as topological indices or topological descriptors
Another vertex degree-based topological index that keeps the spirit of Randic index is the atom bond connectivity index
Summary
Around the center of a century ago, theoretical experts found some interesting relationships between different properties of organic substances and those of molecular structure by analyzing a few invariants of the underlying molecular graph. The mathematical form [12] of this index is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dμðGÞdνðGÞ Another vertex degree-based topological index that keeps the spirit of Randic index is the atom bond connectivity index. We compute the degree-based topological indices, namely, Randic or connectivity index, Zagreb indices, Narumi-Katayama and multiplicative Zagreb indices, atom bond connectivity index, augmented Zagreb index, geometric arithmetic index, harmonic index, and sum connectivity index for two special families of graphs of diameter three. These graphs are undirected having no loops and multiple edges.
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