12.11.3: Formula Review
12.2 Graph Structures
For the Sum of Degrees Theorem, or
The number of edges in a complete graph with vertices is the sum of the whole numbers from 1 to , .
The number of edges in a complete graph with vertices is .
12.7 Hamilton Cycles
The number of ways to arrange distinct objects is .
The number of distinct Hamilton cycles in a complete graph with vertices is .
12.9 Traveling Salesperson Problem
- In a complete graph with vertices, the number of distinct Hamilton cycles is .
- In a complete graph with vertices, there are at most different weights of Hamilton cycles.
12.10 Trees
- The number of edges in a tree graph with vertices is . A connected graph with n vertices and edges is a tree graph.