On the Exact Values of HZ-Index for the Graphs under Operations

Abstract

Topological index (TI) is a function from the set of graphs to the set of real numbers that associates a unique real number to each graph, and two graphs necessarily have the same value of the TI if these are structurally isomorphic. In this note, we compute the HZ−index of the four generalized sum graphs in the form of the various Zagreb indices of their factor graphs. These graphs are obtained by the strong product of the graphs G and DkG, where Dk∈Sk,Rk,Qk,Tk represents the four generalized subdivision-related operations for the integral value of k≥1 and DkG is a graph that is obtained by applying Dk on G. At the end, as an illustration, we compute the HZ−index of the generalized sum graphs for exactly k=1 and compare the obtained results.