o Theorem 5.9: Let G be a simple graph with n vertices. where n>2 G has a hamilton circuit if for any two vertices u and y of g that are not adjacent, d(u)+d(v2n 8,d(u)=d(v) u and v are not adjacent, d(u)+d(v)=6<8 But there is a hamilton circuit in the graph Note: 1)ifG has a Hamilton circuit then g has a Hamilton path Hamilton circuit.v,v,v..v.v 1 Hamilton path:V1,V2, V3,.Vns 2)IfG has a Hamilton path, then G has a Hamilton circuit or has not any Hamilton circuit 7❖ Theorem 5.9: Let G be a simple graph with n vertices, where n>2. G has a Hamilton circuit if for any two vertices u and v of G that are not adjacent, d(u)+d(v)≥n. n=8,d(u)=d(v)=3, u and v are not adjacent, d(u)+d(v)=6<8, But there is a Hamilton circuit in the graph. Note:1)if G has a Hamilton circuit , then G has a Hamilton path Hamilton circuit :v1 ,v2 ,v3 ,…vn ,v1 Hamilton path:v1 ,v2 ,v3 ,…vn , 2)If G has a Hamilton path, then G has a Hamilton circuit or has not any Hamilton circuit