The harmonic index of graphs based on some operations related to the lexicographic product

The harmonic index of a graph G is defined as the sum of the weights frac{2}{deg _G(u)+deg _G(v)} of all edges uv of G, where deg _G(u) denotes the degree of a vertex u in G. In this paper, we investigate the harmonic index of graphs based on operations related to the lexicographic product, subdivision graph, t-subdivision graph, vertex-semitotal graph, edge-semitotal graph and total graph