Research on the Nonplanarity of the Petersen Graph

The Petersen graph plays an important role in graph theory because of its properties, especially the property of nonplanarity. This paper discusses the nonplanarity of the Peterson graph fully and deeply. We creatively propose the concept of hereditary in graph theory. We found that the nonplanarity of a graph have the hereditary property by intensively researching. In addition, we in turn proved the nonplanarity of the Petersen graph by using the hereditary property. We also define the H graph and discuss some properties of it.