Graph theory worksheet with answers

Free printable Graph theory worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy

A simple graph has 6 vertices with degrees 3, 3, 2, 2, 1, 1. How many edges |E| does it have?

deg: 3, 3, 2, 2, 1, 1
|E| =
2.Easy
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Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
3.Medium

A tree has 3 vertices of degree 3, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 3
L =
4.Medium

A connected graph has 20 vertices and 26 edges. How many edges k must be removed to leave a spanning tree?

|V| = 20|E| = 26
k =
5.Hard
ABCDEF

How many closed walks of length 3 start and end at B? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =
6.Hard
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Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 7|E| = 11
W =

Answer key

  1. 1. |E| = 6
  2. 2. F
  3. 3. L = 5
  4. 4. k = 7
  5. 5. N = 2
  6. 6. W = 36

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