Some Results About Degree Sums Of Independent Sets Of Vertices

In this paper we mainly prove the following results about degreesums of independent sets of vertices:Let G be a 4 - connected 1 - tough graphwith n vertices such that and ,then G ishamiltonian;Let G be a 4 - connected l - tough nonhamiltonian graph with n vertices,C is a longest cycle of G,if ,then C is a dominating cycle of G;Let G be a graph with with n vertices,and contain a longest cycle C which is a dominating cycle of G,if vo - V(C),A = N(V0),then (V - V(C))A+ is a independent sets of vertices.Futhermore,we present a conjecture:Let G be a 4 - connected,1 - tough graphwith n vertices such that ,then c(G) min...