12.11.3: Formula Review

Contemporary Mathematics · LibreTexts

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    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.

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