The 2-Domination and 2-Bondage Numbers of Grid Graphs

Details The 2-Domination and 2-Bondage Numbers of Grid Graphs The 2-Domination and 2-Bondage Numbers of Grid Graphs

2012-04-20

arxiv.org/abs/1204.4514v1

Mathematics

Combinatorics

Scientific paper

Let $p$ be a positive integer and $G=(V,E)$ be a simple graph. A subset $D\subseteq V$ is a $p$-dominating set if each vertex not in $D$ has at least $p$ neighbors in $D$. The $p$-domination number $\g_p(G)$ is the minimum cardinality among all $p$-dominating sets of $G$. The $p$-bondage number $b_p(G)$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with a $p$-domination number greater than the $p$-domination number of $G$. In this note we determine the 2-domination number $\g_2$ and 2-bondage number $b_2$ for the grid graphs $G_{m,n}=P_m\times P_n$ for $2\leq m\leq 4$.

Affiliated with

Also associated with

No associations

Rating

The 2-Domination and 2-Bondage Numbers of Grid Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The 2-Domination and 2-Bondage Numbers of Grid Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The 2-Domination and 2-Bondage Numbers of Grid Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-5148