| 图$P_m\times P_n, P_m\times C_n$ 和C_m\times C_n$}的邻点可区别全色数的注记 |
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| 引用本文： | 陈祥恩,张忠辅,孙宜蓉.图$P_m\times P_n, P_m\times C_n$ 和C_m\times C_n$}的邻点可区别全色数的注记[J].数学研究及应用,2008,28(4):789-798. |
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| 作者姓名： | 陈祥恩 张忠辅 孙宜蓉 |
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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;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;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(No.10771091); 甘肃省教育厅科研项目(No.0501-02). |
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| 摘 要： | 设 $G$ 是一个简单图. 设$f$是从$V(G) \cup E(G)$到 $\{1, 2,\ldots, k\}$的一个映射.对任意的 $v\in V(G)$, 设$C_f(v)=\{f(v)\}\cup \{f (vw)|w\in V(G),vw\in E(G)\}$ . 如果 $f$ 是一个 $k$-正常全染色, 且对 $u, v\in V(G),uv\in E(G)$, 有 $C_f(u)\neq C_f(v)$, 那么称 $f$ 为$k$-邻点可区别全染色 (简记为$k$-$AVDTC$). 设
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| 关 键 词： | 图 全染色 邻点可区别全染色 邻点可区别全色数. |
| 收稿时间： | 2006/9/12 0:00:00 |
| 修稿时间： | 2007/10/28 0:00:00 |
A Note on Adjacent-Vertex-Distinguishing Total Chromatic Numbers for $P_m\times P_n, P_m\times C_n$ and $C_m\times C_n$ |
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| CHEN Xiang En,ZHANG Zhong Fu and SUN Yi Rong.A Note on Adjacent-Vertex-Distinguishing Total Chromatic Numbers for $P_m\times P_n, P_m\times C_n$ and $C_m\times C_n$[J].Journal of Mathematical Research with Applications,2008,28(4):789-798. |
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| Authors: | CHEN Xiang En ZHANG Zhong Fu and SUN Yi Rong |
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| Institution: | College of Mathematics and Information Science, Northwest Normal University, Gansu 730070, China;College of Mathematics and Information Science, Northwest Normal University, Gansu 730070, China; Institute of Applied Mathematics, Lanzhou Jiaotong University, Gansu 730070, China;College of Mathematics and Information Science, Northwest Normal University, Gansu 730070, China |
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| Abstract: | Let $G$ be a simple graph. Let $f$ be a mapping from $V(G) \cup E(G)$ to $\{1, 2,\ldots, k\}$. Let $C_f(v)=\{f(v)\}\cup \{f (vw)|w\in V(G), vw\in E(G)\}$ for every $v\in V(G)$. If $f$ is a $k$-proper-total-coloring, and for $u, v\in V(G), uv\in E(G)$, we have $C_f(u)\neq C_f(v)$, then $f$ is called a $k$-adjacent-vertex-distinguishing total coloring ($k$-$AVDTC$ for short). Let $\chi_{at} (G)= \min\{k|G$ have a $k$-adjacent-vertex-distinguishing total coloring$\}$. Then $\chi_{at} (G)$ is called the adjacent-vertex-distinguishing total chromatic number ($AVDTC$ number for short). The $AVDTC$ numbers for $P_m\times P_n, P_m\times C_n$ and $C_m\times C_n$ are obtained in this paper. |
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| Keywords: | total coloring adjacent-vertex-distinguishing total coloring adjacent-vertex-distinguishing total chromatic number |
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