1) Every path is bipartite.
2) Let G be a bipartite graph with partile set X and Y then
∑v∈ X deg(V) = ∑v∈ Y deg(V)
3)Theorem1: Let G be a graph in which all vertices have degree at least 2 then G contain a cycle.
Theorem2: If G is hamiltonian graph then any super graph G' G⊆ G' where G' is obtained by adding new edges between non adjacent vertices of G then G' is also hamiltonian graph