A dominating set S of a graph G is said to be an isolate dominating set of G if the induced subgraph < S > has atleast one isolated vertex. A dominating set S of a graph G is said to be an unique isolate dominating set (UIDS) of G if has exactly one isolated vertex. A d o m i n a t i n g s e t S o f a gr a p h G i s s a i d t o b e a n u n i q u e i s o l a te d o m i n a t i n g s e t ( U ID S ) o f G i f < S > h a s e x a c t l y o n e i s o l a t e d v e r t e x . If a graph G admits UIDS S and x is the isolated vertex in < S >, then S−{x} is a minimum total dominating set in G−N[a]. An UIDS S issaid to be minimal if no propersubset of S is an UIDS. The minimum cardinality of a minimal UIDS of G is called the UID number, denoted by γU (G).T h e m a x i m u m ca r d i n a l i t y o f a m i n im a l U ID S o f G i s c a l l e d t h e u p p e r U ID n u m b e r , d e n o t e d b y 0 ( ) U  G . In this paper we found UIDS in Power of a Cycle Cn k , UIDS in some Families of Graphs like Sun graph, Comb graph and Helm graph, we give an upper bound for the UID number of Cn k . Also, we identify some sub families of Cn k admits UIDS.