@ARTICLE{Amalorpava Jerline,
author = {Amalorpava Jerline, J. and Benedict Michaelraj, L. and },
title = {On Harmonic Index and Diameter of Unicyclic Graphs},
volume = {11},
number = {1},
abstract ={The Harmonic index $ H(G) $ of a graph $ G $ is defined as the sum of the weights $ dfrac{2}{d(u)+d(v)} $ of all edges $ uv $ of $G$, where $d(u)$ denotes the degree of the vertex $u$ in $G$. In this work, we prove the conjecture $dfrac{H(G)}{D(G)} geq dfrac{1}{2}+dfrac{1}{3(n-1)} $ given by Jianxi Liu in 2013 when G is a unicyclic graph and give a better bound $ dfrac{H(G)}{D(G)}geq dfrac{1}{2}+dfrac{2}{3(n-2)}$, where $n$ is the order and $D(G)$ is the diameter of the graph $G$. },
URL = {http://ijmsi.ir/article-1-645-en.html},
eprint = {http://ijmsi.ir/article-1-645-en.pdf},
journal = {Iranian Journal of Mathematical Sciences and Informatics},
doi = {10.7508/ijmsi.2016.01.010},
year = {2016}
}