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
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Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 7
Σ deg =
2.Easy

How many edges |E| does the complete bipartite graph K4,6 have?

K4,6
|E| =
3.Medium

A tree has 3 vertices of degree 3, 3 vertices of degree 4, 4 vertices of degree 5, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 33 × deg 44 × deg 5
L =
4.Medium

A tree has 2 vertices of degree 5, 3 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

2 × deg 53 × deg 2
L =
5.Hard
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Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 4; A itself is round 1.

start: Around 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
6.Hard
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Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 5|E| = 7
W =

Answer key

  1. 1. Σ deg = 20
  2. 2. |E| = 24
  3. 3. L = 23
  4. 4. L = 8
  5. 5. D
  6. 6. W = 35

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