On Harmonic Index and Diameter of Unicyclic Graphs
Author(s):
Abstract:
The Harmonic index $ H(G) $ of a graph $ G $ is defined as the sum of the weights $ dfrac{2}{d(u)(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}痺{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}痺{2}{3(n-2)}$, where $n$ is the order and $D(G)$ is the diameter of the graph $G$.
Keywords:
Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:11 Issue: 1, May 2016
Pages:
115 to 122
https://www.magiran.com/p1527375