University of Isfahan Transactions on Combinatorics 2251-8657 6 4 2017 12 01 The harmonic index of subdivision graphs 15 27 21471 10.22108/toc.2017.21471 EN Bibi Naimeh Onagh Golestan University Journal Article 2016 09 07 ‎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. ‎harmonic index‎ ‎subdivision‎ ‎$S$-sum‎ ‎inverse degree‎ ‎Zagreb index https://toc.ui.ac.ir/article_21471_6d4574ac2fe03052a0872fb991c96309.pdf