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若干倍图的邻点可区别Ⅵ-全染色
引用本文:孙亮萍,强会英,王成利,文飞,张园萍.若干倍图的邻点可区别Ⅵ-全染色[J].数学的实践与认识,2012,42(6):223-232.
作者姓名:孙亮萍  强会英  王成利  文飞  张园萍
作者单位:兰州交通大学数理与软件工程学院,甘肃兰州,730070
基金项目:国家自然科学基金,宁夏大学科学研究基金
摘    要:图的一个边正常的全染色满足相邻点的色集合不同时被称为邻点可区别Ⅵ-全染色,把所用的最少颜色数称为邻点可区别Ⅵ-全色数,其中任意一点的色集合为点上与关联边所染的颜色构成的集合.应用构造邻点可区别Ⅵ-全染色函数法得到了路、圈、星和扇的倍图的邻点可区别Ⅵ-全色数,进一步验证图的邻点可区别Ⅵ-全染色猜想.

关 键 词:倍图  邻点可区别Ⅵ-全染色  邻点可区别Ⅵ-全色数

On a Number of Adjacent Vertex Distinguishing Ⅵ-total Coloring of Double Graphs
SUN Liang-ping , QIANG Hui-ying , WANG Cheng-li , WEN Fei , ZHANG Yuan-ping.On a Number of Adjacent Vertex Distinguishing Ⅵ-total Coloring of Double Graphs[J].Mathematics in Practice and Theory,2012,42(6):223-232.
Authors:SUN Liang-ping  QIANG Hui-ying  WANG Cheng-li  WEN Fei  ZHANG Yuan-ping
Institution:(School of Mathematics,Physics and Software Engineering,Lanzhou Jiaotong University,Lanzhou 730070, China)
Abstract:Let G be a simple graph,k is a positive integer.f is a mapping from V(G) U E(G) to {1,2,…,k} such that(f)uv,uw∈E(G),v≠w,f(uv)≠f(uw);fuv∈E(G),C(u)≠C(v). we say that f is the adjacent vertex distinguishing E-total coloring of G.Where C{u) = {f(u)}\J{f(uv)\uv f E(G)}.The minimal number of k is called the adjacent vertex distinguishing E-total chromatic number of G.In this paper,the adjacent vertex distinguishing Vl-total chromatic number of the double graph of path,circle,star and fan are discussed by constructing the function of adjacent vertex distinguishingⅥ-total coloring,and furthermore, the conjecture of adjacent vertex distinguishingⅥ-total coloring is checked.
Keywords:Double graph  adjacent vertex distinguishing VI-total coloring  adjacent vertex distinguishing VI-total chromatic number
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