The following graph has 45 vertices

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May 11th, 2015

The sum of degrees is 4 * BLANK = BLANK so the number of edges is BLANK by theorem 2.6

 every vertex has degree 4, so each vertex "owns" half each of 4 different edges.

The Handshaking Theorem gives the precise relation between the number of edges in a graph and the sum of the degree of the vertices of a graph. If you know the degree of each vertex, then, you know the sum of the degrees in the graph, and hence the number of edges.

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May 11th, 2015

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