Domination Value in $P_2 \square P_n$ and $P_2 \square C_n$

Details Domination Value in $P_2 \square P_n$ and $P_2 \square C_n$ Domination Value in $P_2 \square P_n$ and $P_2 \square C_n$

2011-09-27

arxiv.org/abs/1109.5908v2

Mathematics

Combinatorics

17 pages, 7 figures, v2: a few minor changes made, mostly fixing typographical errors. This is the final version, to appear in

Scientific paper

A set $D \subseteq V(G)$ is a \emph{dominating set} of a graph $G$ if every vertex of $G$ not in $D$ is adjacent to at least one vertex in $D$. A \emph{minimum dominating set} of $G$, also called a $\gamma(G)$-set, is a dominating set of $G$ of minimum cardinality. For each vertex $v \in V(G)$, we define the \emph{domination value} of $v$ to be the number of $\gamma(G)$-sets to which $v$ belongs. In this paper, we find the total number of minimum dominating sets and characterize the domination values for $P_2 \square P_n$ and $P_2 \square C_n$.

Affiliated with

Also associated with

No associations

Rating

Domination Value in $P_2 \square P_n$ and $P_2 \square C_n$ 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 Domination Value in $P_2 \square P_n$ and $P_2 \square C_n$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Domination Value in $P_2 \square P_n$ and $P_2 \square C_n$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-63053