On the harmonic index of graph operations

Abstract

‎The harmonic index of a connected graph G ‎, ‎denoted by H(G) ‎, ‎is‎ ‎defined as H(G)=∑ uv∈E(G) 2d u +d v ‎ ‎where d v is the degree of a vertex v in G‎. ‎In this paper‎, ‎expressions for the Harary indices of the‎ ‎join‎, ‎corona product‎, ‎Cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.

Keywords

• harmonic index
• Graph operations
• topological indices
• graphs