A graph with Hamilton cycles is called a Hamilton graph.

Theorem 1 If graph G =

Theorem 2 Let G have a simple graph with n nodes. If the sum of the degrees of each pair of nodes in G is greater than or equal to n- 1, there is a Hamilton path in G. ..

Theorem 3 Let G be a simple graph with n nodes. If the sum of the degrees of each pair of nodes in G is greater than or equal to N, there is a Hamiltonian cycle in G. ..

Definition 2 given graph g =

Theorem 4 A simple graph is Hamiltonian if and only if its closure is Hamiltonian.