# In a group of 26 people, is it possible for each person to shake hands with exactly 3 other people?

In a group of 26 people, is it possible for each person to shake hands with exactly 3 other people?

Does anybody know how to solve this?

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This is basically the question whether there exists a cubic graph with 26 vertices. A natural generalization is the question whether it is possible to construct a cubic graph for each even number of vertices - see this question: math.stackexchange.com/questions/412374/… (Handshake lemma easily implies that we cannot have a cubic graph with odd number of vertices.) –  Martin Sleziak Apr 27 '14 at 9:04
I wonder whether this should be closed as a duplicate. (The other question is clearly more general.) –  Martin Sleziak Apr 27 '14 at 10:31
@Did As you pointed out, my answer was wrong. I am abot to delete it. Thanks. –  Jay Apr 28 '14 at 12:46

Note that this is the case for any $n$-gon where $n\equiv 0\pmod{2}$ and $n>3$.