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Discrete Mathematics

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Let G be a graph with vertex set V = { v1, v2, v3, v4, v5}.

If the degrees of the vertices are 1, 2, 1, 3, 1, respectively, is G a tree? Why or why not?

  • Discrete Mathematics -

    By definition, a tree is a connected acyaclic graph.

    One of the sufficient properties of a tree is that the number of edges equals the number of vertices minus one.

    Note: number of edges = (sum of degrees of all vertices)/2.

  • Discrete Mathematics -

    MathMate: Thank you!

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