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arxiv: 1204.3313 · v1 · pith:2X7KNAILnew · submitted 2012-04-15 · 🧮 math.CO

Note on the harmonic index of a graph

Aleksandar Ilic This is my paper
classification 🧮 math.CO
keywords harmonicindexgraphnoteapplboundsdefineddegree
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The harmonic index of a graph $G$ is defined as the sum of weights $\frac{2}{deg(v) + deg(u)}$ of all edges $uv$ of $E (G)$, where $deg (v)$ denotes the degree of a vertex $v$ in $V (G)$. In this note we generalize results of [L. Zhong, The harmonic index on graphs, Appl. Math. Lett. 25 (2012), 561--566] and establish some upper and lower bounds on the harmonic index of $G$.

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