Signed total domination number of a graph

Zelinka, Bohdan. "Signed total domination number of a graph." Czechoslovak Mathematical Journal 51.2 (2001): 225-229. <http://eudml.org/doc/30630>.

@article{Zelinka2001,
abstract = {The signed total domination number of a graph is a certain variant of the domination number. If $v$ is a vertex of a graph $G$, then $N(v)$ is its oper neighbourhood, i.e. the set of all vertices adjacent to $v$ in $G$. A mapping $f: V(G) \rightarrow \lbrace -1, 1\rbrace $, where $V(G)$ is the vertex set of $G$, is called a signed total dominating function (STDF) on $G$, if $\sum _\{x \in N(v)\} f(x) \ge 1$ for each $v \in V(G)$. The minimum of values $\sum _\{x \in V(G)\} f(x)$, taken over all STDF’s of $G$, is called the signed total domination number of $G$ and denoted by $\gamma _\{\mathrm \{s\}t\}(G)$. A theorem stating lower bounds for $\gamma _\{\mathrm \{s\}t\}(G)$ is stated for the case of regular graphs. The values of this number are found for complete graphs, circuits, complete bipartite graphs and graphs on $n$-side prisms. At the end it is proved that $\gamma _\{\mathrm \{s\}t\}(G)$ is not bounded from below in general.},
author = {Zelinka, Bohdan},
journal = {Czechoslovak Mathematical Journal},
keywords = {signed total dominating function; signed total domination number; regular graph; circuit; complete graph; complete bipartite graph; Cartesian product of graphs; signed total dominating function; signed total domination number; regular graph; circuit; complete graph; complete bipartite graph; Cartesian product of graphs},
language = {eng},
number = {2},
pages = {225-229},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Signed total domination number of a graph},
url = {http://eudml.org/doc/30630},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - Signed total domination number of a graph
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 225
EP - 229
AB - The signed total domination number of a graph is a certain variant of the domination number. If $v$ is a vertex of a graph $G$, then $N(v)$ is its oper neighbourhood, i.e. the set of all vertices adjacent to $v$ in $G$. A mapping $f: V(G) \rightarrow \lbrace -1, 1\rbrace $, where $V(G)$ is the vertex set of $G$, is called a signed total dominating function (STDF) on $G$, if $\sum _{x \in N(v)} f(x) \ge 1$ for each $v \in V(G)$. The minimum of values $\sum _{x \in V(G)} f(x)$, taken over all STDF’s of $G$, is called the signed total domination number of $G$ and denoted by $\gamma _{\mathrm {s}t}(G)$. A theorem stating lower bounds for $\gamma _{\mathrm {s}t}(G)$ is stated for the case of regular graphs. The values of this number are found for complete graphs, circuits, complete bipartite graphs and graphs on $n$-side prisms. At the end it is proved that $\gamma _{\mathrm {s}t}(G)$ is not bounded from below in general.
LA - eng
KW - signed total dominating function; signed total domination number; regular graph; circuit; complete graph; complete bipartite graph; Cartesian product of graphs; signed total dominating function; signed total domination number; regular graph; circuit; complete graph; complete bipartite graph; Cartesian product of graphs
UR - http://eudml.org/doc/30630
ER -