Some Importent points of graphs

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