Comparative Study of Generalized Sum Graphs via Degree-Based Topological Indices

Abstract

In theoretical chemistry, topological indices (TIs) have important role to predict various physical and structural properties of the study under molecular graphs. Among all topological indices, Zagreb-type indices have been used more effectively in the chemical literature. In this paper, we have computed first Zagreb, second Zagreb, forgotten, and hyper Zagreb indices of the generalized $Q$ -sum graph $\left(H_{1_{\left(Q_{\alpha }\right)}}\left[H_2\right]\right)$ in the form of different TIs of its basic graphs, where $\alpha \ge 1$ is a positive integer. This family of graphs is obtained by the lexicographic product of the graph $Q_{\alpha }\left(H_1\right)$ and $H_2$ , where $Q_{\alpha }\left(H_1\right)$ is constructed with the help of the generalized line superposition operation $Q_{\alpha }$ on $H_1$ . As a conclusion, we also checked the correlation between predefined graph $H_1\left[H_2\right]$ under the operation of lexicographic product $H_1$ and $H_2$ with newly defined generalized $Q$ -sum graphs $\left(H_{1_{\left(Q_{\alpha }\right)}}\left[H_2\right]\right)$ using linear regression models of various degree-based TIs.