# Article

Full entry | PDF   (0.2 MB)
Keywords:
signed majority total dominating function; signed majority total domination number
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 $\gamma _{{\mathrm maj}}^{{\,\mathrm t}}(G)$.
References:
[1] B.  Zelinka: Signed total domination number of a graph. Czechoslovak Math. J. 51 (2001), 225–229. DOI 10.1023/A:1013782511179 | MR 1844306 | Zbl 0977.05096
[2] I.  Broere, J. H.  Hattingh, M. A.  Henning and A. A. McRae: Majority domination in graphs. Discrete Math. 138 (1995), 125–135. DOI 10.1016/0012-365X(94)00194-N | MR 1322087
[3] J. H.  Hattingh: Majority domination and its generalizations. Domination in Graphs: Advanced Topics, T. W.  Haynes, S. T.  Hedetniemi,and P. J. Slater (eds.), Marcel Dekker, New York, 1998. MR 1605689 | Zbl 0891.05042
[4] T. S.  Holm: On majority domination in graph. Discrete Math. 239 (2001), 1–12. DOI 10.1016/S0012-365X(00)00370-8 | MR 1850982

Partner of