Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1395
1
1
gregorian
2016
4
1
11
1
online
1
fulltext
en
On Harmonic Index and Diameter of Unicyclic Graphs
تخصصي
Special
پژوهشي
Research paper
<p>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 $G$.</p>
Harmonic index, Diameter, Unicyclic graph.
115
122
http://ijmsi.ir/browse.php?a_code=A-10-1060-1&slc_lang=en&sid=1
J.
Amalorpava Jerline
jermaths@gmail.com
10031947532846002889
10031947532846002889
Yes
Holy Cross College
L.
Benedict Michaelraj
10031947532846002890
10031947532846002890
No
Joseph’s College