关于图的符号边全控制数

On Signed Edge Total Domination Numbers of Graphs

中文关键词:  符号边全控制函数  符号边全控制数  边度.

英文关键词:signed edge total dominating function  signed edge total domination number  edge degree.

中文摘要:

      设$G=(V,E)$ 为图，定义函数$f:E\rightarrow \{{-1,1}\} $ ，若对任意边$e\in E(G)$均有 ${\sum_{e^{^{\prime }}\in N(e)} }f(e^{\prime})\geq1$成立，则称该函数为 $G$的符号边全控制函数（SETDF），而$G$ 的符号边全控制数$\gamma_{st}^{\prime}(G)$定义为$\gamma_{st}^{\prime}(G)=min\{\sum_{e\in E(G)}f(e)|f\ is\ an\ SETDF\ of\ G\}$。我们得到了符号边全控制数一些新的下界。 }

英文摘要:

      Let $G=(V,E)$ be a graph. A function $f:E\rightarrow \{-1,1\} $ is said to be a signed edge total dominating function (SETDF) of $G$ if ${\sum_{e^{^{\prime }}\in N(e)} }f(e^{\prime})\geq 1$ holds for every edge $e\in E(G)$. The signed edge total domination number $\gamma_{st}^{\prime}(G)$ of $G$ is defined as $\gamma_{st}^{\prime}(G)=\min\{\sum_{e\in E(G)}f(e)|f$ is an SETDF of $G\}$. In this paper we obtain some new lower bounds of $\gamma_{st}^{\prime}(G)$.