The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
نویسندگان
چکیده
منابع مشابه
On Harmonic Index and Diameter of Unicyclic Graphs
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 dfra...
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ژورنال
عنوان ژورنال: Journal of Mathematics
سال: 2021
ISSN: 2314-4785,2314-4629
DOI: 10.1155/2021/6680242