| 一类化学图及其线图的Wiener指数 |
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| 引用本文： | 邓汉元. 一类化学图及其线图的Wiener指数[J]. 湖南师范大学自然科学学报, 2009, 32(3) |
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| 作者姓名： | 邓汉元 |
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| 作者单位： | 湖南师范大学数学与计算机科学学院,中国长沙,410081 |
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| 基金项目： | 国家自然科学基金资助项目，湖南省自然科学基金资助项目 |
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| 摘 要： | 图G=(V,E)的Wiener指数W(G)是一个基于距离的拓扑指数,它是G中所有顶点之间的距离之和.对于任意整数n,证明了存在无限多个圈秩为2平面二部化学图,其Wiener指数与它的线图的Wiener指数之差是n,且其线图也是化学图;部分解决了A.D.Dobrynin和L.S.Mernikow提出的一个公开问题.
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| 关 键 词： | 化学图 线图 Wiener指数 圈秩 |
The Wiener Index of a Class of Chemical Graphs and Their Line Graphs |
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| DENG Han-yuan. The Wiener Index of a Class of Chemical Graphs and Their Line Graphs[J]. Journal of Natural Science of Hunan Normal University, 2009, 32(3) |
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| Authors: | DENG Han-yuan |
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| Abstract: | The Wiener index W(G) of a graph G = (V,E) is a distance-based topological index defined as the sum of distances between all pairs of vertices in G. For any integer n, an infinite family of planar and bipartite chemical graphs with cyclomatic number two are constructed such that their line graphs are also chemical graphs, and the difference of the Wiener indices between the graphs and their line graphs is n. This affirms partly an open problem proposed by A. D. Dobry-nin and L. S. Mernikov. |
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| Keywords: | chemical graph line graph Wiener index cyclomatic number |
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