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

Eunjeong Yi

paper

Domination Value in $P_{2} □ P_{n}$ and $P_{2} □ C_{n}$

arXiv:1109.5908

Abstract

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 $γ (G)$ -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 $γ (G)$ -sets to which $v$ belongs. In this paper, we find the total number of minimum dominating sets and characterize the domination values for $P_{2} □ P_{n}$ and $P_{2} □ C_{n}$ .

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

Domination Value in P2​□Pn​ and P2​□Cn​

Abstract

References in corpus (2)

Domination Value in $P_{2} □ P_{n}$ and $P_{2} □ C_{n}$