Indicate whether the following statements are true or false: a. If e is a minimum-weight edge in a connected weighted graph, it must be among edges of at least one minimum spanning tree of the graph. b. If e is a minimum-weight edge in a connected weighted graph, it must be among edges of each minimum spanning tree of the graph. E. If edge weights of a connected weighted graph are all distinct, the graph must have exactly one minimum spanning tree.

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Author:James Kurose, Keith Ross
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**Problem 6A (Minimum Spanning Tree)**

*Please provide brief reason to support your answer.*

Indicate whether the following statements are true or false:

a. If \( e \) is a minimum-weight edge in a connected weighted graph, it must be among edges of at least one minimum spanning tree of the graph.

b. If \( e \) is a minimum-weight edge in a connected weighted graph, it must be among edges of each minimum spanning tree of the graph.

c. If edge weights of a connected weighted graph are all distinct, the graph must have exactly one minimum spanning tree.

d. If edge weights of a connected weighted graph are not all distinct, the graph must have more than one minimum spanning tree.
Transcribed Image Text:**Problem 6A (Minimum Spanning Tree)** *Please provide brief reason to support your answer.* Indicate whether the following statements are true or false: a. If \( e \) is a minimum-weight edge in a connected weighted graph, it must be among edges of at least one minimum spanning tree of the graph. b. If \( e \) is a minimum-weight edge in a connected weighted graph, it must be among edges of each minimum spanning tree of the graph. c. If edge weights of a connected weighted graph are all distinct, the graph must have exactly one minimum spanning tree. d. If edge weights of a connected weighted graph are not all distinct, the graph must have more than one minimum spanning tree.
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