1. **Problem Statement:** Determine which of the given graphs are Euler graphs. 2. **Definition:** An Euler graph is a graph containing an Eulerian circuit, which is a cycle that uses every edge exactly once and starts and ends at the same vertex. 3. **Key Rule:** A connected graph has an Eulerian circuit if and only if every vertex has an even degree (an even number of edges). 4. **Check each graph:** - **Graph A:** Vertices degrees: A(4), B(2), C(2), D(4), E(3), F(2). Vertex E has degree 3 (odd), so no Eulerian circuit. - **Graph B:** Degrees: A(1), B(4), C(1), D(1), E(1). Vertices A, C, D, E have odd degrees, so no Eulerian circuit. - **Graph C:** Degrees: A(3), B(3), C(4), D(2), E(2), F(2), G(3), H(2). Vertices A, B, G have odd degrees, so no Eulerian circuit. - **Graph D:** Degrees: A(2), B(3), C(2), D(3), E(3), F(3), G(3). Vertices B, D, E, F, G have odd degrees, so no Eulerian circuit. - **Graph E:** Degrees: A(2), B(3), C(1), D(1), E(2). Vertices B, C, D have odd degrees, so no Eulerian circuit. - **Graph F:** Degrees: A(2), B(2), C(2), D(3), E(3), F(3), G(2), H(2), I(2). Vertices D, E, F have odd degrees, so no Eulerian circuit. 5. **Conclusion:** None of the graphs have all vertices with even degree, so none are Euler graphs. **Final answer:** No graph among A, B, C, D, E, F is an Euler graph.