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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.
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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