完全二部图K5,n的点可区别IE-全染色 |
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引用本文: | 何文玉,陈祥恩. 完全二部图K5,n的点可区别IE-全染色[J]. 山东大学学报(自然科学版), 2009, 0(2): 91-96 |
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作者姓名: | 何文玉 陈祥恩 |
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作者单位: | 西北师范大学数学与信息科学学院,甘肃兰州730070 |
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基金项目: | 国家自然科学基金资助项目(10771091) |
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摘 要: | 设G是简单图,图G的一个k-点可区别IE-全染色(简记为k-VDIET染色)f是指一个从V(G)∪E(G)到{1,2,…,k}的映射,且满足:A↓uv∈E(G),有f(u)≠f(v);A↓u,v∈V(G),u≠v,有C(u)≠C(v),其中C(u)={f(u)}∪{f(uv)|uv∈E(G)}。数min{k}G有一个k-VDIET染色}称为图G的点可区别IE-全色数,记为χut^ie(G)。本文给出了完全二部图K5,n(n≥6)的点可区别IE-全色数。
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关 键 词: | 图 点可区别IE-全染色 点可区别IE-全色数 完全二部图 |
Vertex distinguishing IE-total chromatic numbers of complete bipartite graph K5,n |
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Affiliation: | HE Wen-yu, CHENG Xiang-en(College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China) |
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Abstract: | Let G be a simple graph. An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C (u) be the set of colors of vertex u and edges incident to u under f. For an IE- total coloring f of G using k colors, if C (u) ≠ C (v) for any two different vertices u and v of V(G), then f is called a k-ver- tex-distingnishing IE-total-coloring of G, or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χvt^ie (G), and it is called the VDIET chromatic number of G. VDIET chromatic numbers for the complete bipartite graph K5. n ( n≥ 6) were given. |
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Keywords: | graphs vertex-distinguishing IE-total coloring vertex-distinguishing IE-total chromatic number complete bipartite graph |
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