Abstract: It is proved that there exists no finite solvable group G with the following as its character degree graph: .____.____.____. . The result solves an important open problem by Huppert and provides more evidence supporting the well-known conjecture which claims that the diameter of the degree graph of any finite solvable group is at most 2.

Key words: finite solvable group, degree graph, representation, module

摘要： 对具有4个顶点的指标阶图进行了研究，证明了下述定理：不存在有限可解G，使得G的指标阶图同构于下面的图： ·——·——·——·这一结果解决了Huppert在1990年提出的一个公开问题。该结果和所用方法也为解决著名的指标图半径猜想开辟了道路。

关键词: 有限可解群, 指标阶图, 表示, 模