دوره 11، شماره 1 - ( 1-1395 )                   جلد 11 شماره 1 صفحات 115-122 | برگشت به فهرست نسخه ها


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چکیده:  

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 $G$.

نوع مطالعه: پژوهشي | موضوع مقاله: تخصصي