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 [tex]G[/tex] be a graph with vertices [tex]v_1,v_2,\cdots,v_n[/tex]
Then [tex]\sum_{i=1}^ndeg(v_i)=2e\\[/tex] where [tex]e[/tex] is the number of edges of the graph. Since the graph is regular of degree r then all vertices have degree r. Thus,
[tex]\sum_{i=1}^n r=2e\\nr=2e\\e=\frac{nr}{2}[/tex]
