The harmonic index of subdivision graphs

Abstract

‎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 study the harmonic index of subdivision graphs‎, ‎$t$-subdivision graphs and also‎, ‎$S$-sum and $S_t$-sum of graphs‎.