<P> In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of vertices with odd degree (the number of edges touching the vertex). In more colloquial terms, in a party of people some of whom shake hands, an even number of people must have shaken an odd number of other people's hands . </P> <P> The handshaking lemma is a consequence of the degree sum formula (also sometimes called the handshaking lemma), </P> <Dl> <Dd> ∑ v ∈ V deg ⁡ v = 2 E (\ displaystyle \ sum _ (v \ in V) \ deg v = 2 E) </Dd> </Dl> <Dd> ∑ v ∈ V deg ⁡ v = 2 E (\ displaystyle \ sum _ (v \ in V) \ deg v = 2 E) </Dd>

Number of vertices of odd degree in a graph