证明了:如果一个特征标维数图含一个五阶圈,则它必含4个顶点,这4个顶点决定的导出子图的度数和大于8.还证明了含五阶圈的特征标维数图对应的有限可解群的Fitting高不大于4.
The authors prove that a character vertices with the derived subgraph which has Fitting height of a finite solvable group that has degree graph that contains a fifth-order circle must have four the sum of degrees more than 8. And they also prove that the a character degree graph with a fifth-order circle is at most 4.