Let K, be the complete graph on n vertices. a) Draw Kn for n = 1, 2, 3, 4, 5. For each, how many edges are there?

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Let K, be the complete graph on n vertices.
a) Draw K, for n = 1, 2, 3, 4, 5. For each, how many edges are there?
b) Let E (K„) denote the number of edges in K. Write a recurrence relation for E(Kn) along
with initial conditions. (You do not need to prove this formula is correct)
c) Guess an explicit, non-recursive formula for E (Kn) and use induction to prove it using the
recurrence relation from part b. That is, assume the recurrence relation is true and use it to
prove the explicit formula.
Transcribed Image Text:Let K, be the complete graph on n vertices. a) Draw K, for n = 1, 2, 3, 4, 5. For each, how many edges are there? b) Let E (K„) denote the number of edges in K. Write a recurrence relation for E(Kn) along with initial conditions. (You do not need to prove this formula is correct) c) Guess an explicit, non-recursive formula for E (Kn) and use induction to prove it using the recurrence relation from part b. That is, assume the recurrence relation is true and use it to prove the explicit formula.
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