The harmonic index of subdivision graphs

Document Type: Research Paper

Author

Golestan University

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.

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