05925104

j

05925104 Walikar, H. B. Narayankar, Kishori P. Shirakol, Shailaja Shekharappa, H.G. The number of minimum dominating sets in $P_n\times P_2$. Int. J. Math. Comb. 3, 17-21 (2010). 2010 The MADIS of Chinese Academy of Sciences, Beijing EN Smarandachely $k$-dominating set Smarandachely $k$-domination number dominating sets dominating number 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 $P_n\times P_2$.