find four spanning trees for the connected graph. select all that apply.
find four spanning trees for the connected graph. select all that apply.
Answer
Explanation:
Step1: Recall spanning - tree definition
A spanning tree of a connected graph is a sub - graph that is a tree and connects all the vertices of the original graph. It has no cycles.
Step2: Analyze option A
It connects all 4 vertices (A, B, C, D) and has no cycles, so it is a spanning tree.
Step3: Analyze option B
It connects all 4 vertices and has no cycles, so it is a spanning tree.
Step4: Analyze option C
It connects all 4 vertices and has no cycles, so it is a spanning tree.
Step5: Analyze option D
It connects all 4 vertices and has no cycles, so it is a spanning tree.
Step6: Analyze option E
It has a cycle (e.g., A - C - B - D - A), so it is not a spanning tree.
Step7: Analyze option F
It has a cycle (e.g., A - C - B - D - A), so it is not a spanning tree.
Answer:
A. A - B - D - C, B. A - C - D - B, C. A - C - B - D, D. A - B - C - D