%0 Journal Article %A Amalorpava Jerline, J. %A Benedict Michaelraj, L. %T On Harmonic Index and Diameter of Unicyclic Graphs %J Iranian Journal of Mathematical Sciences and Informatics %V 11 %N 1 %U http://ijmsi.ir/article-1-645-en.html %R 10.7508/ijmsi.2016.01.010 %D 2016 %K Harmonic index, Diameter, Unicyclic graph., %X 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 $G$. %> http://ijmsi.ir/article-1-645-en.pdf %P 115-122 %& 115 %! %9 Research paper %L A-10-1060-1 %+ Holy Cross College %G eng %@ 1735-4463 %[ 2016