Volume :1 , Issue :1 ,Page :19-28

Abstract :et G be a conn ected graph. Let  ,  i ,  t ,  e and  p denote respectively the domination number, the independent domination number, th e total domination number, the connected domination number and the perfect domination number of G. The n-cube Q n is the graph, whose vertex set is the set of all n-dime nsional Boolean vectors with two ver tices being joined if and only if they differ in exactly one coor dinate. Hamming proved that Q n has a perfect dominating set if and only if n = 2 k  1. Here, it is proved that  (Q n ) = 2 n–k for n = 2 k . Bounds for  i (Q n ),  c (Q n ),  t (Q n ) and  p (Q n ) are also found out. Finally, it is conjectured that  (Q n ) =  (Q n–1 ) +  (2 n–1  (Q n–1 ))/ (n  1)  for 2 k +1  n  2 k+1 –2, where  x  denote the least inte ger not less than x.