Question
Download Solution PDFA complete graph of n nodes will have _______ number of spanning trees.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 1: nn−2
Key Points
- The number of spanning trees in a **complete undirected graph** with n nodes is given by **Cayley’s formula**:
- This applies specifically to **complete graphs**, where every pair of distinct vertices is connected by a unique edge.
Examples:
- For n = 3 → spanning trees
- For n = 4 → spanning trees
Additional Information
- Option 2 (1): Only true for trees with exactly n − 1 edges, not for complete graphs.
- Option 3 (0): Invalid; a complete graph always has spanning trees if n ≥ 2.
- Option 4 (n/2): Not mathematically correct or relevant to spanning trees.
Hence, the correct answer is: option 1: nn−2
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