Extremal values on the harmonic number of trees |
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| Authors: | Qiong Fan Qin Zhao |
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| Affiliation: | 1. School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China;2. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;3. School of Mathematics and Statistics, Hubei University, Wuhan 430062, China |
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| Abstract: | Let G=(V(G), E(G)) be a simple connected graph. The harmonic number of G, denoted by H(G), is defined as the sum of the 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, some extremal problems on the harmonic number of trees are studied. The extremal values on the harmonic number of trees with given graphic parameters, such as pendant number, matching number, domination number and diameter, are determined. The corresponding extremal graphs are characterized, respectively. |
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| Keywords: | trees harmonic number matching number domination number diameter |
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