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There are different mathematical tools to establish a numeric correlation between a chemical structure and its properties. A topological index is such a successful tool. It represents a graph in form of a single real number. In QSAR/QSPR study, the bioactivity of chemical compounds is predicted, using physico-chemical properties and topological indices. In this area of research, graph theory plays a vital role. The four operations on graphs were defined by Eliasi and Taeri in 2009. Imran et al. studied Cartesian product of the four operations on graph and computed bounds for some degree-based topological indices in 2017. In this paper, we extend this study for the lexicographic product of graphs to determine bounds of Zagreb indices, multiple Zagreb indices, and  F -index for four sums of connected graphs.

Bounds of Some Degree Based Indices of Lexicographic Product of Some Connected Graphs