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The degree sum formula states that, given a graph <math>G=(V, E)</math>,

The degree sum formula states that, given a graph <math>G=(V, E)</math>,

'''<font color="#ff8000">度和公式 Degree Sum Formula</font>'''表明，给定一个图<math>G=(V, E)</math>,

'''<font color="#ff8000">度和公式 Degree Sum Formula</font>'''表明，任意给定一个图<math>G=(V, E)</math>,都有

The formula implies that in any undirected graph, the number of vertices with odd degree is even. This statement (as well as the degree sum formula) is known as the handshaking lemma. The latter name comes from a popular mathematical problem, to prove that in any group of people the number of people who have shaken hands with an odd number of other people from the group is even.

The formula implies that in any undirected graph, the number of vertices with odd degree is even. This statement (as well as the degree sum formula) is known as the handshaking lemma. The latter name comes from a popular mathematical problem, to prove that in any group of people the number of people who have shaken hands with an odd number of other people from the group is even.

此公式表明，在任何无向图中，拥有奇数度值的顶点的个数是偶数。这一阐释（以及度和公式)被称为'''<font color="#ff8000">握手引理 Handshaking Lemma</font>'''。该名称来自一个有趣的数学问题，即证明无论该群体内有多少人，与奇数个人握过手的人数总是偶数。

此公式表明，在任何无向图中，拥有奇数度值的顶点的个数是偶数。这一阐释（以及度和公式)被称为'''<font color="#ff8000">握手引理 Handshaking Lemma</font>'''。该名称来自一个有趣的数学问题，即求证无论该群体内有多少人，与奇数个人握过手的人数总是偶数。

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