12. Recall that a graph is a pair of sets V, E where EC2V and every...
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12. Recall that a graph is a pair of sets V, E where EC2V and every element of E has precisely two elements. (a) Prove that Ucpe CV. (b) For every v € V define d = #{e € E ve e}. Prove that Evev dy = 2#E. (c) A graph is complete if E = {{x,y} xe V and y € Vand a #y}. Prove by induction that if V is finite and the graph is complete then #E=n(n-1)/2. 12. Recall that a graph is a pair of sets V, E where EC2V and every element of E has precisely two elements. (a) Prove that Ucpe CV. (b) For every v € V define d = #{e € E ve e}. Prove that Evev dy = 2#E. (c) A graph is complete if E = {{x,y} xe V and y € Vand a #y}. Prove by induction that if V is finite and the graph is complete then #E=n(n-1)/2.
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Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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