Construction of Petersen graph via graph product and correlation of topological descriptors of Petersen graph in terms of cyclic graph C 5

Abstract Graph product yields a new structure from two initial given structures. The computation of topological indices for these sophisticated structures using the graph product is a critical endeavor. Petersen graph is a structure which consists of ten vertices and fifteen edges. It is commonly used as a counter example to graph theory conjectures. In this paper, we generate simple Petersen graph by using graph product and then explicit expressions of the first and second Zagreb indices, forgotten topological index, first hyper and first reformulated Zagreb index, reduced second Zagreb index and Y-index of the Peterson graph in terms of cyclic graph C5 are computed.