On the \(n\)-vertex trees with sixth to fifteenth maximum harmonic indices. (English) Zbl 1463.05063
Summary: The harmonic index of a graph \(G\) is denoted by \(H(G)\) and is defined as \(H(G)=\sum_{uv\in E(G)} \frac{2}{d_u+d_v}\), where \(d_u\), \(d_v\) denote the degrees of the vertices \(u\), \(v\), respectively, of \(G\) and \(E(G)\) is the edge set of \(G\). In this paper, the graphs having sixth to fifteenth maximum harmonic indices are characterized from the class of all \(n\)-vertex trees for sufficiently large \(n\).
MSC:
| 05C07 | Vertex degrees |
| 05C35 | Extremal problems in graph theory |
| 05C05 | Trees |
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
Software:
GRAFFITIReferences:
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