Question

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?

Answer 1

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.

Answer 2

MathMate: Thank you!