1. **State the problem:** Determine if the sequence $5, 4, 3, 2, 1, 0$ is graphic, meaning it can represent the degree sequence of a simple graph. 2. **Recall the definition:** A sequence is graphic if there exists a simple graph whose vertex degrees correspond exactly to the sequence. 3. **Apply the Havel-Hakimi algorithm:** - Start with the sequence sorted in non-increasing order: $5, 4, 3, 2, 1, 0$ - Remove the first degree $d=5$ and subtract 1 from the next $d=5$ degrees. 4. **Check feasibility:** The sequence has 6 terms, so the maximum degree is 5, which is valid since a vertex can connect to at most 5 others. 5. **Subtract 1 from the next 5 degrees:** - The next 5 degrees are $4, 3, 2, 1, 0$ - Subtracting 1 gives $3, 2, 1, 0, -1$ 6. **Check for negative degrees:** The last term is $-1$, which is invalid. 7. **Conclusion:** Since the sequence after subtraction contains a negative number, the original sequence is **not graphic**. **Final answer:** The sequence $5, 4, 3, 2, 1, 0$ is not graphic, so no graph can be drawn with this degree sequence.