| 一类完全三部图的色唯一性 |
| |
| 引用本文： | 苏克义,陈祥恩.一类完全三部图的色唯一性[J].数学的实践与认识,2011,41(2). |
| |
| 作者姓名： | 苏克义 陈祥恩 |
| |
| 作者单位： | 1. 宁夏银川市第六中学,宁夏,银川,750011
2. 西北师范大学,数学与信息科学学院,甘肃,兰州,730070 |
| |
| 基金项目： | 国家自然科学基金(10771091); 甘肃省教育厅科研项目(0501-02) |
| |
| 摘 要： | 用P(G,λ)表示简单图G的色多项式.设G是一个给定的简单图,若对任意简单图H,当P(H,λ)=P(G,λ)时都有H和G同构(记为H≌G),则称图G是色唯一的.本文证明了以下结果:设n,k,△都为非负整数,其中k≥0,△∈{4,5},若n≥1/3k~2+1/3△~2-1/3k△-1/3k-1/3△+4/3,则完全三部图K(n,n+△,n+k)是色唯一的.同时还给出了一个猜想.
|
| 关 键 词： | 完全三部图 色多项式 色唯一图 色划分 |
Chromatic Uniqueness of a Kind of Complete Tripartite Graphs |
| |
| SU Ke-yi,CHEN Xiang-en.Chromatic Uniqueness of a Kind of Complete Tripartite Graphs[J].Mathematics in Practice and Theory,2011,41(2). |
| |
| Authors: | SU Ke-yi CHEN Xiang-en |
| |
| Institution: | SU Ke-yi~1,CHEN Xiang-en~2 (1.Yinchuan Sixth Middle School,Yinchuan 750011,China) (2.College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China) |
| |
| Abstract: | Let P(G,λ) denote the chromatic polynomial of a simple graph G.Graph G issaid to be chromatically unique if for any simple graph H,P(H,λ) = P(G,λ) implies that His isomorphic to G(or simply H≌G).The following result has been proved in this paper:fornonnegative integers n,k,△,where k≥0,△∈{4,5},if n≥1/3k~2+ 1/3△~2-1/3k△-1/3k-1/3△+4/3,then the complete tripartite graph K(n,n +△,n + k) is chromatically unique.Furthermore,we present a conjecture. |
| |
| Keywords: | complete tripartite graph chromatic polynomial chromatically unique graph color partition |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
