Sufficient Condition for Complete Graphs and Hamiltonian Graphs

In 1856, Hamiltonian introduced the Hamiltonian Graph where a Graph which is covered all the vertices without repetition and end with starting vertex. In this paper I would like to prove that every Complete Graph ‘G’ having n ? 5 vertices, such that n is odd. If for all pairs of nonadjacent vertices u, v one has du + dv ? n − 2, then G has a Hamiltonian path.