图论的Show that a simple graph with at least two vertices there must be two vertices that have the same degree

分类: 作业答案 • 2022-02-21 12:35:31

问题描述：

图论的
Show that a simple graph with at least two vertices there must be two vertices that have the same degree

答

设G是一个n个顶点的简单图,若G含孤立顶点,则它的最大度不超过n-2,由鸽笼原理,一定存在两个点的度数相同；若G不含孤立顶点,则它的最小度大于等于1,最大度小于等于n-1,由鸽笼原理,也一定存在两个点的度数相同.