find four spanning trees for the connected gr...

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