Math 801 -graph Theory
نویسنده
چکیده
Assignment 1 François Séguin Question 1 (a) We know that for any simple graph X, v∈V (X) d(v) = 2 |E(X)|. In particular, the sum must be even. Here, summing over all the degrees of the vertices yield a total degree of 41, which is odd. Therefore, there is no such simple graph. The Handshake Lemma for bipartite graphs states that, if A and B are the disjoint independent set of vertices of the graph X, then v∈A d(v) = v∈B d(v) = |E(X)| .
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