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A graph G has 21 Edges, 3 vertices of degree 4 and other vertices are of degree 3. Find the number of vertices in G.
Ans: It is specified that graph G has 21 edges, so total degree of graph is 42. It is as well given that three vertices are of degree 4 and other vertices are degree 3. Assume number of vertices of degree 3 is y. After that
3y + 4x3 = 42
⇒ y = (42 - 12) / 3 = 10.
Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2
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