corollary 1: Let G be a simple grap with n vertices. n>2.g has a hamilton circuit if each vertex has degree greater than or equal to n/2 g Proof: If any two vertices of G are adjacent then G has a Hamilton circuit V1V2,V3y…VnV1° .s If g has two vertices u and y that are not adjacent, then d(u+d(v2n. &By the theorem 5.9g has a hamilton circuit .&K has a hamilton circuit where n>3❖ Corollary 1: Let G be a simple graph with n vertices, n>2. G has a Hamilton circuit if each vertex has degree greater than or equal to n/2. ❖ Proof: If any two vertices of G are adjacent ,then G has a Hamilton circuit v1 ,v2 ,v3 ,…vn ,v1。 ❖ If G has two vertices u and v that are not adjacent, then d(u)+d(v)≥n. ❖ By the theorem 5.9, G has a Hamilton circuit. ❖ Kn has a Hamilton circuit where n≥3