Let's look at the graph edges step by step! 🎉 **Step 1:** Imagine you have 6 vertices: $v_1, v_2, v_3, v_4, v_5, v_6$. **Step 2:** We write the edges as pairs from start to end vertices: - $e_1$ goes from $v_1$ to $v_2$ - $e_2$ goes from $v_1$ to $v_3$ - $e_3$ goes from $v_2$ to $v_4$ - $e_4$ goes from $v_3$ to $v_4$ - $e_5$ goes from $v_4$ to $v_5$ - $e_6$ goes from $v_3$ to $v_6$ - $e_7$ goes from $v_1$ to $v_6$ - $e_8$ goes from $v_6$ to $v_5$ - $e_9$ goes from $v_2$ to $v_5$ **Step 3:** Write these as a matrix with top row start vertices and bottom row end vertices: $$\begin{bmatrix} 1 & 1 & 2 & 3 & 4 & 3 & 1 & 6 & 2 \\ 2 & 3 & 4 & 4 & 5 & 6 & 6 & 5 & 5 \end{bmatrix}$$ **Step 4:** Check the options: Option b: $$\begin{bmatrix} 1 & 1 & 1 & 2 & 2 & 3 & 3 & 4 & 5 \\ 2 & 3 & 6 & 3 & 5 & 5 & 6 & 5 & 6 \end{bmatrix}$$ Compare with our matrix: - We have $e_3$ from 2 to 4, but option b has 2 to 3. Option a: $$\begin{bmatrix} 1 & 1 & 1 & 2 & 2 & 3 & 3 & 4 & 6 \\ 2 & 3 & 7 & 3 & 5 & 5 & 6 & 5 & 6 \end{bmatrix}$$ - The edges 7 and 6 don't match our vertices. Option c and d also have vertices like 9 which do not exist. **Step 5:** So, the correct matrix is: $$\begin{bmatrix} 1 & 1 & 2 & 3 & 4 & 3 & 1 & 6 & 2 \\ 2 & 3 & 4 & 4 & 5 & 6 & 6 & 5 & 5 \end{bmatrix}$$ This matrix is not exactly in the options, but option b is closest except for some mistakes. **Final answer:** None of the given options exactly match the graph edges. Great job checking carefully! 🎯 Keep up the good work!