On the Harmonic Index of Unicyclic Conjugated Molecules
نویسندگان
چکیده
The harmonic index H(G) of a graph G is defined as the sum of weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we first present a sharp lower bound on the harmonic index of unicyclic conjugated graphs (unicyclic graphs with a perfect matching). Also a sharp lower bound on the harmonic index of unicyclic graphs is given in terms of the order and given size of matching.
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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