7. We define a forest to be a graph with no cycles. a. Explain why this is a good name. That is, explain why a forest is a union of trees. b. Suppose F is a forest consisting of m trees and v vertices. How many edges does F have? Explain. c. Prove that any graph G with v vertices and e edges that satisfies v

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7. We define a forest to be a graph with no cycles.
a. Explain why this is a good name. That is, explain why a forest is a union of
trees.
b. Suppose Fis a forest consisting of m trees and v vertices. How many
edges does F have? Explain.
c. Prove that any graph G with v vertices and e edges that satisfies v <e+ 1
must contain a cycle (i.e., not be a forest).
> Hint
Transcribed Image Text:7. We define a forest to be a graph with no cycles. a. Explain why this is a good name. That is, explain why a forest is a union of trees. b. Suppose Fis a forest consisting of m trees and v vertices. How many edges does F have? Explain. c. Prove that any graph G with v vertices and e edges that satisfies v <e+ 1 must contain a cycle (i.e., not be a forest). > Hint
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