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If G has n vertices and is regular of degree r, how many edges has G?

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Answer:

We know that the sum of the degrees of the vertices of the graph is twice the number of edges of the graph.

Let
G be a graph with vertices
v_1,v_2,\cdots,v_n

Then
\sum_(i=1)^ndeg(v_i)=2e\\ where
e is the number of edges of the graph. Since the graph is regular of degree r then all vertices have degree r. Thus,


\sum_(i=1)^n r=2e\\nr=2e\\e=(nr)/(2)

User Claude Hasler
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