A Sufficient Condition Of Hamilton Graph On The Condition Of 1-tough

We have known that 1-tough graphs and hamiltonian graphs are two kinds of im-portant graphs. Researchers find the important connection between 1-tough graphs and hamiltonian graphs, in the process of looking for the necessary and sufficient condition of Hamilton graphs. D. Bauer and E. Schmeichel proved G is hamiltoni-an graph, when G is 1-tough graph and δ≥(n+k-2)/3. B.Wei promoted the above conclusion and got G is hamiltonian graph, when G is 1-tough graph and σ3≥n+k-2. He proposed a conjecture that G is hamiltonian graph, when G is n≥3,1-tough graph and σ3≥ max{n, n+k-3}. In this article, we prove the conjecture.