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圈和完全图的点可区别VE-全染色(英文)
引用本文:辛小青,陈祥恩,王志文.圈和完全图的点可区别VE-全染色(英文)[J].数学季刊,2012(1):92-97.
作者姓名:辛小青  陈祥恩  王志文
作者单位:College of Mathematics and Information Science,Northwest Normal University;School of Mathematics Science,Baotou Teacher’s College;School of Mathematics and Computer Sciences,Ningxia University
基金项目:Supported by the NNSF of China(61163037,61163054);Supported by the Scientific Research Foundation of Ningxia University((E):ndzr09-15)
摘    要:Let G be a simple graph of order at least 2.A VE-total-coloring using k colors of a graph G is a mapping f from V (G) E(G) into {1,2,···,k} such that no edge receives the same color as one of its endpoints.Let C(u)={f(u)} {f(uv) | uv ∈ E(G)} be the color-set of u.If C(u)=C(v) for any two vertices u and v of V (G),then f is called a k-vertex-distinguishing VE-total coloring of G or a k-VDVET coloring of G for short.The minimum number of colors required for a VDVET coloring of G is denoted by χ ve vt (G) and it is called the VDVET chromatic number of G.In this paper we get cycle C n,path P n and complete graph K n of their VDVET chromatic numbers and propose a related conjecture.

关 键 词:graphs  VE-total  coloring  vertex-distinguishing  VE-total  coloring  vertexdistinguishing  VE-total  chromatic  number

Vertex-distinguishing VE-total Colorings of Cycles and Complete Graphs
XIN Xiao-qing,CHEN Xiang-en,WANG Zhi-wen.Vertex-distinguishing VE-total Colorings of Cycles and Complete Graphs[J].Chinese Quarterly Journal of Mathematics,2012(1):92-97.
Authors:XIN Xiao-qing  CHEN Xiang-en  WANG Zhi-wen
Institution:1.College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China;2.School of Mathematics Science,Baotou Teacher’s College,Baotou 014030,China;3.School of Mathematics and Computer Sciences,Ningxia University,Yinchuan 750021,China)
Abstract:Let G be a simple graph of order at least 2.A VE-total-coloring using k colors of a graph G is a mapping f from V (G) E(G) into {1,2,· · ·,k} such that no edge receives the same color as one of its endpoints.Let C(u)={f(u)} {f(uv)|uv ∈ E(G)} be the color-set of u.If C(u)=C(v) for any two vertices u and v of V (G),then f is called a k-vertex-distinguishing VE-total coloring of G or a k-VDVET coloring of G for short.The minimum number of colors required for a VDVET coloring of G is denoted by χ ve vt (G) and it is called the VDVET chromatic number of G.In this paper we get cycle C n,path P n and complete graph K n of their VDVET chromatic numbers and propose a related conjecture.
Keywords:graphs  VE-total coloring  vertex-distinguishing VE-total coloring  vertexdistinguishing VE-total chromatic number
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