Inequalities involving independence domination, $f$-domination, connected and total $f$-domination numbers

Zhou, San Ming. "Inequalities involving independence domination, $f$-domination, connected and total $f$-domination numbers." Czechoslovak Mathematical Journal 50.2 (2000): 321-330. <http://eudml.org/doc/30563>.

@article{Zhou2000,
abstract = {Let $f$ be an integer-valued function defined on the vertex set $V(G)$ of a graph $G$. A subset $D$ of $V(G)$ is an $f$-dominating set if each vertex $x$ outside $D$ is adjacent to at least $f(x)$ vertices in $D$. The minimum number of vertices in an $f$-dominating set is defined to be the $f$-domination number, denoted by $\gamma _\{f\}(G)$. In a similar way one can define the connected and total $f$-domination numbers $\gamma _\{c, f\}(G)$ and $\gamma _\{t, f\}(G)$. If $f(x) = 1$ for all vertices $x$, then these are the ordinary domination number, connected domination number and total domination number of $G$, respectively. In this paper we prove some inequalities involving $\gamma _\{f\}(G), \gamma _\{c, f\}(G), \gamma _\{t, f\}(G)$ and the independence domination number $i(G)$. In particular, several known results are generalized.},
author = {Zhou, San Ming},
journal = {Czechoslovak Mathematical Journal},
keywords = {domination number; independence domination number; $f$-domination number; connected $f$-domination number; total $f$-domination number; domination number; independence domination number; -domination number; connected -domination number; total -domination number},
language = {eng},
number = {2},
pages = {321-330},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inequalities involving independence domination, $f$-domination, connected and total $f$-domination numbers},
url = {http://eudml.org/doc/30563},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Zhou, San Ming
TI - Inequalities involving independence domination, $f$-domination, connected and total $f$-domination numbers
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 321
EP - 330
AB - Let $f$ be an integer-valued function defined on the vertex set $V(G)$ of a graph $G$. A subset $D$ of $V(G)$ is an $f$-dominating set if each vertex $x$ outside $D$ is adjacent to at least $f(x)$ vertices in $D$. The minimum number of vertices in an $f$-dominating set is defined to be the $f$-domination number, denoted by $\gamma _{f}(G)$. In a similar way one can define the connected and total $f$-domination numbers $\gamma _{c, f}(G)$ and $\gamma _{t, f}(G)$. If $f(x) = 1$ for all vertices $x$, then these are the ordinary domination number, connected domination number and total domination number of $G$, respectively. In this paper we prove some inequalities involving $\gamma _{f}(G), \gamma _{c, f}(G), \gamma _{t, f}(G)$ and the independence domination number $i(G)$. In particular, several known results are generalized.
LA - eng
KW - domination number; independence domination number; $f$-domination number; connected $f$-domination number; total $f$-domination number; domination number; independence domination number; -domination number; connected -domination number; total -domination number
UR - http://eudml.org/doc/30563
ER -