| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D |
D |
| deepseekr1 | The number of edges in a complete graph with \( n \) vertices is given by the combination formula \( \binom{n}{2} \), which calculates the number of ways to choose 2 vertices out of \( n \) to form an edge. This formula simplifies to \( \frac{n(n-1)}{2} \). For \( n = 10 \): \[ \frac{10 \times 9}{2} = \frac{90}{2} = 45 \] Thus, a complete graph with 10 vertices has **45 edges**. Answer: D |
D |
| gpto1 | D | D |
| GPT-4o | D. 45 | D |
| llama3.1-70B-Instruct | D |
D |
| llama3.1-405B-Instruct | To determine the number of edges in a complete graph with 10 vertices, we can use the formula for the number of edges in a complete graph, which is given by: Number of edges = n(n-1)/2 where n is the number of vertices. Plugging in n = 10, we get: Number of edges = 10(10-1)/2 = 10(9)/2 = 90/2 = 45 Therefore, the correct answer is: D. 45 |
D |
| DeepSeek-Coder-V2 | D. 45 | D |
| Qwen2-72B-Instruct | D. 45 | D |
| baichuan4 | D. 45 | D |
| doubao | D. 45. For a complete graph with n vertices, the number of edges is n(n-1)/2. For a graph with 10 vertices, the number of edges is 10(10-1)/2 = 45. | D |
| minimax | D. 45 A complete graph with n vertices has an edge between every pair of vertices. The number of edges in a complete graph can be calculated using the formula for combinations, since each edge is a combination of 2 vertices from the set of n vertices: Number of edges = n(n - 1) / 2 For a complete graph with 10 vertices: Number of edges = 10(10 - 1) / 2 = 10 * 9 / 2 = 90 / 2 = 45 So, the correct answer is D. 45. |
D |
| kimi | The number of edges in a complete graph can be calculated using the formula for combinations, since each edge is a combination of 2 vertices out of the total number of vertices. The formula for combinations is: \[ \text{Number of combinations} = \frac{n!}{k!(n-k)!} \] For a complete graph, \( n \) is the total number of vertices and \( k \) is the size of the combination (which is 2 for an edge). So the formula simplifies to: \[ \text{Number of edges} = \frac{n(n-1)}{2} \] For a graph with 10 vertices: \[ \text{Number of edges} = \frac{10 \times (10-1)}{2} = \frac{10 \times 9}{2} = \frac{90}{2} = 45 \] Answer: D. 45 |
D |
| wenxinyiyan | D. 45 Explanation: In a complete graph with n vertices, there is an edge connecting every pair of vertices. To count the number of edges, we can use the formula for combinations: C(n, 2) = n * (n - 1) / 2 This formula gives the number of ways to choose 2 items from n items without repetition, which corresponds to the number of edges in a complete graph. Using n = 10, we get: C(10, 2) = 10 * (10 - 1) / 2 = 10 * 9 / 2 = 45 So, a complete graph with 10 vertices has 45 edges. |
D |
| zhipu | To determine the number of edges in a complete graph with \( n \) vertices, we use the formula: \[ \text{Number of edges} = \frac{n(n-1)}{2} \] For a complete graph with 10 vertices (\( n = 10 \)): \[ \text{Number of edges} = \frac{10(10-1)}{2} = \frac{10 \times 9}{2} = \frac{90}{2} = 45 \] Therefore, the correct answer is: D. 45 |
D |
| gpto1 | D | D |
| deepseekv3 | To determine the number of edges in a complete graph with 10 vertices, we use the formula for the number of edges in a complete graph with \( n \) vertices: \[ \text{Number of edges} = \frac{n(n - 1)}{2} \] For \( n = 10 \): \[ \text{Number of edges} = \frac{10 \times 9}{2} = \frac{90}{2} = 45 \] Therefore, the correct answer is: D. 45 |
D |