| 二树的ABC指标 |
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| 引用本文： | 于四勇,赵海兴,毛亚平,肖玉芝.二树的ABC指标[J].数学研究及应用,2016,36(2):140-150. |
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| 作者姓名： | 于四勇 赵海兴 毛亚平 肖玉芝 |
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| 作者单位： | 青海师范大学计算机学院, 青海 西宁 810008,青海师范大学数学系, 青海 西宁 810008,青海师范大学数学系, 青海 西宁 810008,青海师范大学计算机学院, 青海 西宁 810008 |
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| 基金项目： | 国家自然科学基金项目(Grant Nos.61164005; 61440005;11161037), 教育部重点实验室和创新团队资助(Grant No.IRT_15R40), 教育部春晖计划项目(Grant No.Z2014022), 青海省自然科学基金项目(Grant Nos.2013-Z-Y17; 2014-ZJ-907; 2014-ZJ-721). |
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| 摘 要： | The atom-bond connectivity(ABC) index of a graph G, introduced by Estrada,Torres, Rodr′?guez and Gutman in 1998, is defined as the sum of the weights(1/di+1/dj-2/didj )~(1/2) of all edges vivj of G, where di denotes the degree of the vertex vi in G. In this paper, we give an upper bound of the ABC index of a two-tree G with n vertices, that is, ABC(G) ≤(2n- 4)2~(1/2)/2+(2n-4)~(1/2)/n-1. We also determine the two-trees with the maximum and the second maximum ABC index.
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| 关 键 词： | 图 2-树 ABC指标 |
| 收稿时间： | 2/9/2015 12:00:00 AM |
| 修稿时间： | 2015/9/14 0:00:00 |
On the Atom-Bond Connectivity Index of Two-Trees |
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| Siyong YU,Haixing ZHAO,Yaping MAO and Yuzhi XIAO.On the Atom-Bond Connectivity Index of Two-Trees[J].Journal of Mathematical Research with Applications,2016,36(2):140-150. |
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| Authors: | Siyong YU Haixing ZHAO Yaping MAO and Yuzhi XIAO |
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| Institution: | School of Computer, Qinghai Normal University, Qinghai 810008, P. R. China,Department of Mathematics, Qinghai Normal University, Qinghai 810008, P. R. China,Department of Mathematics, Qinghai Normal University, Qinghai 810008, P. R. China and School of Computer, Qinghai Normal University, Qinghai 810008, P. R. China |
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| Abstract: | The atom-bond connectivity $(ABC)$ index of a graph $G$, introduced by Estrada, Torres, Rodr\'{\i}guez and Gutman in 1998, is defined as the sum of the weights $\sqrt{\frac{1}{d_i}+\frac{1}{d_j}-\frac{2}{{d_i}{d_j}}}$ of all edges ${v_i}{v_j}$ of $G$, where $d_i$ denotes the degree of the vertex $v_i$ in $G$. In this paper, we give an upper bound of the $ABC$ index of a two-tree $G$ with $n$ vertices, that is, $ABC(G)\le(2n-4)\frac{\sqrt{2}}{2}+\frac{\sqrt{2n-4}}{n-1}$. We also determine the two-trees with the maximum and the second maximum ABC index. |
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| Keywords: | graph two-trees atom-bond connectivity index |
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