1. **Problem Statement:** Find an Euler path in the given graph with vertices O, L, M, K, P, and N and edges as described. 2. **Euler Path Definition:** An Euler path is a trail in a graph that visits every edge exactly once. For an Euler path to exist, the graph must be connected, and either exactly zero or two vertices have an odd degree (number of edges). 3. **Step 1: Calculate the degree of each vertex:** - O: connected to L, K, P, N → degree 4 - L: connected to O, M, P, N → degree 4 - M: connected to L, P → degree 2 - K: connected to O, P → degree 2 - P: connected to O, L, M, K → degree 4 - N: connected to O, L → degree 2 4. **Step 2: Check the number of vertices with odd degree:** - All vertices have even degree (2 or 4). 5. **Step 3: Conclusion:** - Since all vertices have even degree, an Euler circuit (and thus an Euler path) exists. 6. **Step 4: Find an Euler path (Euler circuit) example:** One possible Euler path starting at O: $$O \to L \to M \to P \to K \to O \to N \to L \to P$$ This path uses every edge exactly once. **Final answer:** An Euler path exists, for example: $$O \to L \to M \to P \to K \to O \to N \to L \to P$$