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

Title:

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

Creator:

Zhou, San Ming

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c447dcd3-5739-4388-bd42-e27bfa9bf4b9
uuid:c447dcd3-5739-4388-bd42-e27bfa9bf4b9

Subject:

domination number, independence domination number, $f$-domination number, and total $f$-domination number

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

321-330

Source:

Czechoslovak Mathematical Journal | 2000 Volume:50 | Number:2

Harvested from:

CDK

Metadata only:

false