On signed majority total domination in graphs

summary:We initiate the study of signed majority total domination in graphs. Let $G=(V,E)$ be a simple graph. For any real valued function $f\: V \rightarrow \mathbb{R}$ and ${S\subseteq V}$, let $f(S)=\sum _{v\in S}f(v)$. A signed majority total dominating function is a function $f\: V\rightarrow \lbrace -1,1\rbrace $ such that $f(N(v))\ge 1$ for at least a half of the vertices $v\in V$. The signed majority total domination number of a graph $G$ is $\gamma _{{\mathrm maj}}^{{\,\mathrm t}}(G)=\min \lbrace f(V)\mid f$ is a signed majority total dominating function on $G\rbrace $. We research some properties of the signed majority total domination number of a graph $G$ and obtain a few lower bounds of $\gamma _{{\mathrm maj}}^{{\,\mathrm t}}(G)$