On Signed Edge Total Domination Numbers of Graphs

Abstract:

      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 $\gamma_{st}^{\prime}(G)$.