The general Randić index of trees with given number of pendent vertices
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- 作者：Qing Cui<sup> ; sup><sup>cui@nuaa.edu.cnsup> ; Lingping Zhong <sup>zhong@nuaa.edu.cnsup>
- 关键词：Randić index ; General Randić index ; Tree ; Chemical tree
- 刊名：Applied Mathematics and Computation
- 出版年：2017
- 出版时间：1 June 2017
- 年：2017
- 卷：302
- 期：Complete
- 页码：111-121
- 全文大小：811 K
- 卷排序：302
文摘
The general Randić index of a graph G is defined as Rα(G)=∑uv∈E(G)α(d(u)d(v)),Rα(G)=∑uv∈E(G)(d(u)d(v))α, where d(u) denotes the degree of a vertex u in G and α is a real number. In this paper, we determine the maximum general Randić indices of trees and chemical trees with n vertices and k pendent vertices for 4≤k≤⌊n+23⌋ and α0 ≤ α < 0, where α0≈−0.5122α0≈−0.5122 is the unique non-zero root of the equation 6·α4−20·α9+10·α12−α16+5·α24=06·4α−20·9α+10·12α−16α+5·24α=0. The corresponding extremal graphs are also characterized.