UPPER BOUNDS ON THE HARMONIC STATUS INDEX

The harmonic status index of a simple connected graph G is defined as the sum of the weights 2/ sigma G(u)+sigma G(v) over all edges uv of G, where sigma G(u) denotes the status of the vertex u in G which is the sum of distances between u and all other vertices of G. In this paper, we present upper bounds on the harmonic status index of some families of graph products in terms of certain structural invariants such as the order, size, maximum degree, inverse status and harmonic status index of their components. The graph products considered here are sum, disjunction, symmetric difference, Indu-Bala product, corona product, Cartesian product, lexicographic product, and strong product. Some applications of the obtained results are also presented as corollaries.