A Series of New Necessary Conditions for a Graph to Be Hamiltonian
一些新的Hamilton图的必要条件

It is not solved what specific property of a Hamiltonian graph is. Depending on structural properties of a graph, a way to divide vertices of the graph into several groups is designed. It is studied that the relationship between number of vertices and bounds of the before layer and number of vertices and bounds of the next layer. The relationship between a graph and its Hamiltonian evolutionary graph is researched. Some results concerning necessary condition for a graph to be Hamiltonian are proved. It is proved that the new necessary conditions for a graph to be Hamiltonian are not only efficient but also convenient. We show how the results give an easy proof of the nonexistence of a Hamiltonian cycle in the Petersen graph.