@article {
author = {Liang, Meili and Cheng, Bo and Liu, Jianxi},
title = {Solution to the minimum harmonic index of graphs with given minimum degree},
journal = {Transactions on Combinatorics},
volume = {7},
number = {2},
pages = {25-33},
year = {2018},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2017.101076.1462},
abstract = {The harmonic index of a graph $G$ is defined as $ H(G)=\sum\limits_{uv\in E(G)}\frac{2}{d(u)+d(v)}$, where $d(u)$ denotes the degree of a vertex $u$ in $G$. Let $\mathcal{G}(n,k)$ be the set of simple $n$-vertex graphs with minimum degree at least $k$. In this work we consider the problem of determining the minimum value of the harmonic index and the corresponding extremal graphs among $\mathcal{G}(n,k)$. We solve the problem for each integer $k (1\le k\le n/2)$ and show the corresponding extremal graph is the complete split graph $K_{k,n-k}^*$. This result together with our previous result which solve the problem for each integer $k (n/2 \le k\le n-1)$ give a complete solution of the problem.},
keywords = {harmonic index,minimum degree,extremal graphs},
url = {https://toc.ui.ac.ir/article_22272.html},
eprint = {https://toc.ui.ac.ir/article_22272_28d4f6f37d2867d952c1398e234888f8.pdf}
}