应用数学学报 2013, Vol. 36 Issue (4): 761-768    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索  | 1. 上海立信会计学院数学与信息学院, 上海, 201620;
2. 上海大学理学院, 上海, 200444
The Two-variable Chromatic Polynomial of Regular Tree Study
TANG Xiaoqing1, LIU Nianzu1, WANG Hanxing1, BAI Yanqin2
1. School of Mathematics & information, Shanghai Lixin University of Commerce, Shanghai, 201620;
2. College of Sciences, Shanghai University, Shanghai, 200444
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 服务 把本文推荐给朋友 加入我的书架 加入引用管理器 E-mail Alert RSS 作者相关文章 唐晓清 刘念祖 王汉兴 白延琴

Abstract： Recently, Klaus Dohmen et al proposed a notion of new two-variable chromatic polynomials. In order to further study the related properties of this notion, we have carried out theoretical derivation and computer verified, then we have achieved a general compute formula for the two-variable chromatic polynomials of any graph, calling Reduction Edge Formula, we give it a forthright proof. By using the formula repeatedly, people can get any graph's two-variable chromatic polynomials conveniently. Based on this formula, we got the two-variable chromatic polynomial compute formula of some special graphs and disconnected multi-branch graph. Also, we got a Delete Vertex Formula of a graph which contains disconnected multi-partite as its subgraphs, and a vertex linked to each subgraph. We study the sum of coefficients to two-variable chromatic polynomials and we get a important conclusion for it. Then we propose a new notion of regular tree, and we study its new two-variable chromatic polynomial compute formula and many other properties. Later, we propose integral subgraph of a regular tree , and we study the new two-variable chromatic polynomial of it, also we got its compute formula and many other important properties.

 引用本文: 唐晓清,刘念祖,王汉兴等. 正则树的双变量色多项式研究[J]. 应用数学学报, 2013, 36(4): 761-768. TANG Xiaoqing,LIU Nianzu,WANG Hanxing et al. The Two-variable Chromatic Polynomial of Regular Tree Study[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(4): 761-768.

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