Which of the following statements is not true with spanning trees and forests (in graph theory)?...
- Which of the following statements is not true with spanning trees and forests (in graph theory)? Also, explain why it is not true.
- A spanning tree of a connected graph is a spanning subgraph that is a tree.
- A spanning tree is not unique when the graph is a tree.
- A spanning forest of a graph is also a spanning subgraph that is a forest.
- A spanning subgraph of a tree contains all the vertices of the tree.
Homework Answers
Correct option: b
Explanation:
A spanning tree covers all the vertices of the graph with a minimal set of edges. So, a spanning tree is a subgraph that is a tree.
When the graph is a tree then there may be only one spanning tree because spanning tree is also a tree and a tree has a minimal set of edges that cover all vertices. So, if the graph is already a tree then the spanning tree will be unique.
Spanning forest is a collection of spanning-tree.
A spanning subgraph of a tree covers all the vertices of the tree.
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