Search code examples
algorithmmathgraph-theoryverticesundirected-graph

Handshaking lemma with 3 people?

Handshaking lemma states in an undirected graph an even number of vertices must have odd degree.

However 3 people shaking hands with each other, 6 hand shakes, or two a each. So there are no vertices with odd degree.

Does the handshaking lemma hold true because 0 is even and there are zero vertices of odd degree?

I'm not doubting the lemma is true, just thinking I'm missing something really obvious.

Solution

  • Does the handshaking lemma hold true because 0 is even and there are zero vertices of odd degree?

    Yes. Since all 3 vertices are of even-degree, so there are zero vertices of odd-degree.

    You're absolutely correct. Same is the case when people = 1.