HZ-Coindex for the Sum-Graphs under Cartesian Product

Abstract

Let G = (V (G), E(G)) be a simple connected graph with V (G) and E(G) as the vertex and edge sets respectively. The physical and structural properties of the graphs are discussed with different mathematical tools, One of them is topological index (TI) and it can be obtained directly from molecular structures and rapidly computed for large number of molecules. Graph operations play an important role in the development of various new classes of graphs. If G is a connected simple graph then we obtained new graphs by applying various operations on G such as S subdivided, R triangle parallel, Q line superposition and T total graphs operations on G. In this paper, we computed the hyper Zagreb coindex of derived graphs in the form of their factor graphs. At the end, we have analyzed our results by the numerical tables for the particular generalized D-sum graphs.