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| 关于几类特殊图的Mycielski图的邻点可区别全色数 | |
| 引用本文： | 陈祥恩,张忠辅,晏静之,张贵仓.关于几类特殊图的Mycielski图的邻点可区别全色数[J].兰州大学学报(自然科学版),2005,41(2):117-122. |
| 作者姓名： | 陈祥恩 张忠辅 晏静之 张贵仓 |
| 作者单位： | 1. 西北师范大学,数学与信息科学学院,甘肃,兰州,730070 2. 西北师范大学,数学与信息科学学院,甘肃,兰州,730070;兰州交通大学,应用数学研究所,甘肃,兰州,730070 3. 兰州大学,数学与统计学院,甘肃,兰州,730000 |
| 基金项目： | Natural Science Foundation of China，甘肃省科技攻关项目，西北师范大学校科研和教改项目，西北师范大学校科研和教改项目 |
| 摘 要： | 设G是一个简单图,f是一个从V(G)∪ E(G)到{1,2,…,k}的映射.对每个v∈V(G),令Cf(v)={f(v)}∪{f(vw)|w∈V(G),vw∈E(G)}.如果f是G的正常全染色且u,v∈V(G),一旦uv∈E(G),就有Cf(u)≠Cf(v),那么称f为G的邻点可区别全染色(简称为k-AVDTC).设xat(G)=min{k|G存在k-AVDTC},则称xat(G)为G的邻点可区别全色数.给出了路、圈、完全图、完全二分图、星、扇和轮的Mycielski图的邻点可区别全色数. |
| 关 键 词： | 图 全染色 邻点可区别全染色 邻点可区别全色数 |
Adjacent-vertex-distinguishing total chromatic numbers on Mycielski's graphs of several kinds of particular graphs |
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| CHEN Xiang-en,ZHANG Zhong-fu,YAN Jing-zhi,ZHANG Gui-cang.Adjacent-vertex-distinguishing total chromatic numbers on Mycielski''''s graphs of several kinds of particular graphs[J].Journal of Lanzhou University(Natural Science),2005,41(2):117-122. | |
| Authors: | CHEN Xiang-en ZHANG Zhong-fu YAN Jing-zhi ZHANG Gui-cang |
| Abstract: | Let G be a simple graph, f be a mapping from V(G) U E(G) to {1, 2, … , k}. Let Cf(v) = {f(v)}∪{f(vw)|w ∈ V(G), vw ∈ E(G)}for every v ∈ V(G). Iff is a k-proper-total-coloring, and for u, v ∈ V(G), uv ∈ E(G), we have Cf(u) ≠ Cf(v), then f is called the k-adjacent-vertex-distinguishing total coloring(k-AVDTC for short). Let xat(G) = min{k|G has a k-adjacent-vertex- distinguishing total coloring}. Then xat(G) is called the adjacent-vertex-distinguishing total chromatic number. The adjacent-vertex-distinguishing total chromatic numbers on Mycielski's graphs of path, cycle, complete graph, complete bipartite graph, star, fan and wheel are presented in this paper. |
| Keywords: | graph total coloring adjacent-vertex-distinguishing total coloring adjacent-vertex-distinguishing total chromatic number |
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