Volume 11, Issue 1 (4-2016)                   IJMSI 2016, 11(1): 115-122 | Back to browse issues page

DOI: 10.7508/ijmsi.2016.01.010

XML Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Amalorpava Jerline J, Benedict Michaelraj L. On Harmonic Index and Diameter of Unicyclic Graphs. IJMSI. 2016; 11 (1) :115-122
URL: http://ijmsi.ir/article-1-645-en.html


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 $G$.

Type of Study: Research | Subject: Special

Add your comments about this article : Your username or Email:
Write the security code in the box

© 2015 All Rights Reserved | Iranian Journal of Mathematical Sciences and Informatics

Designed & Developed by : Yektaweb