\input zb-basic \input zb-ioport \iteman{io-port 05925104} \itemau{Walikar, H. B.; Narayankar, Kishori P.; Shirakol, Shailaja; Shekharappa, H.G.} \itemti{The number of minimum dominating sets in $P_n\times P_2$.} \itemso{Int. J. Math. Comb. 3, 17-21 (2010).} \itemab Summary: A set $S$ of vertices in a graph $G$ is said to be a Smarandachely $k$-dominating set if each vertex of $G$ is dominated by at least $k$ vertices of $S$. The Smarandachely $k$-domination number $\gamma_k(G)$ of $G$ is the minimum cardinality of Smarandachely $k$-dominating sets of $G$. Particularly, if $k=1$, a Smarandachely $k$-dominating set is called a dominating set of $G$ and $gamma_k(G)$ is abbreviated to $\gamma(G)$. In this paper, we get the Smarandachely 1-dominating number, i.e., the dominating number of $P_n\times P_2$. \itemrv{~} \itemcc{} \itemut{Smarandachely $k$-dominating set; Smarandachely $k$-domination number; dominating sets; dominating number} \itemli{} \end