1. **Problem Statement:** Determine if the wiggly edges in each graph (a, b, c, d) form a spanning tree. 2. **Definition and Formula:** A spanning tree of a graph is a subgraph that includes all vertices, is connected, and contains no cycles. For a graph with $n$ vertices, a spanning tree has exactly $n-1$ edges. 3. **Step-by-step Analysis:** - The graphs have vertices $\{A,B,C,D,E,F,I,H\}$, so $n=8$ vertices. - A spanning tree must have $8-1=7$ edges, be connected, and have no cycles. 4. **Graph a:** - Count wiggly edges and check connectivity and cycles. - If wiggly edges do not connect all vertices or form cycles, it is not a spanning tree. 5. **Graph b:** - Repeat the same check. 6. **Graph c:** - Repeat the same check. 7. **Graph d:** - Repeat the same check. **Since the exact wiggly edges are not explicitly described, we cannot definitively conclude for each graph.** **However, the general approach is:** - Count the wiggly edges. - Verify if all 8 vertices are connected by these edges. - Check if the number of edges is 7. - Check for cycles (no cycles allowed). If any condition fails, the wiggly edges do not form a spanning tree. **Final answer:** Without explicit edge data, the method above is how to determine if the wiggly edges form a spanning tree.