吕大梅,林文松,宋增民.完全图的Cantesian积的L(2,1)-圆标定[J].数学研究及应用,2009,29(1):91~98
完全图的Cantesian积的L(2,1)-圆标定
L(2,1)-Circular Labelings of Cartesian Products of Complete Graphs
投稿时间:2006-12-17  修订日期:2007-09-04
DOI:10.3770/j.issn:1000-341X.2009.01.012
中文关键词:  $\lambda_{1}^{2}$-数  $\sigma_{k}^{j}$-数  Cartesian积.
英文关键词:$\lambda_{2,1}$-number  $\sigma_{2,1}$-number  Cartesian product.
基金项目:国家自然科学基金(No.10671033); 东南大学科学基金(No.XJ0607230); 南通大学自然科学基金(No.08Z003).
作者单位
吕大梅 南通大学理学院, 江苏 南通 226001 
林文松 东南大学数学系, 江苏 南京 210096 
宋增民 东南大学数学系, 江苏 南京 210096 
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中文摘要:
      设$j,k$为正整数,图$G$的$L(j,k)\,$-标定是一个满足相邻点的标号差不小于$j$和距离2的两点标号差不小于$k$两个条件的非负整数函数.在所有$L(j,k)\,-$标定对应跨度中最小的跨度称之为$G$的$\lambda^j_k\,$-数. 图$G$的$m$-$L(j,k)$-圆标定是一个函数$f:V(G)\rightarrow \{0,1,2,\cdots,m-1\}$, 且其满足下面两个条件:当$u$和$v$相邻时, $|f(u)-f(v)|_{m}\geq j\,$;当$u$和$v$距离
英文摘要:
      For positive integers $j$ and $k$ with $j\geq k$, an $L(j,k)$-labeling of a graph $G$ is an assignment of nonnegative integers to $V(G)$ such that the difference between labels of adjacent vertices is at least $j$, and the difference between labels of vertices that are distance two apart is at least $k$. The span of an $L(j,k)$-labeling of a graph $G$ is the difference between the maximum and minimum integers it uses. The $\lambda_{j,k}$-number of $G$ is the minimum span taken over all $L(j,k)$-labelings of $G$. An $m$-$(j,k)$-circular labeling of a graph $G$ is a function $f: V(G)\rightarrow \{0,1,2,\ldots,m-1\}$ such that $|f(u)-f(v)|_{m}\geq j$ if $u$ and $v$ are adjacent; and $|f(u)-f(v)|_{m}\geq k$ if $u$ and $v$ are at distance two, where $|x|_{m}=\min\{|x|,m-|x|\}$. The minimum integer $m$ such that there exists an $m$-$(j,k)$-circular labeling of $G$ is called the $\sigma_{j,k}$-number of $G$ and is denoted by $\sigma_{j,k}(G)$. This paper determines the $\sigma_{2,1}$-number of the Cartesian product of any three complete graphs.
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