Discrete Math - Suppose you want to provide a general... ?
Suppose you want to provide a general expression for the number of edges in a complete graph Kn. Explain how you could provide some examples to help you find a pattern. How can you use this pattern to create a formula?
- RealProLv 74 weeks ago
Basic combinatorics yields the answer without "finding patterns". I assume what is meant here is to simply draw them starting from the smallest and explore the results. The differences between the differences of the consecutive terms of a quadratic sequence are constant so that would mean if you were certain that was it, you would have 3 parameters to determine, which could be done with a simple linear system of 3 equations.
- JJLv 74 weeks ago
If a complete graph has n vertices, then each vertex has degree n - 1. The sum of all the degrees in a complete graph, Kn, is n(n-1). The number of edges in a complete graph, Kn, is (n(n - 1)) / 2.