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 4, 3, 3, 2, 2, 2. How many edges |E| does it have?

deg: 4, 3, 3, 2, 2, 2
|E| =
2.Easy

A simple graph has 5 vertices with degrees 3, 2, 2, 2, 1. How many edges |E| does it have?

deg: 3, 2, 2, 2, 1
|E| =
3.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 =
4.Medium

How many different Hamilton circuits H does the complete graph K4 have? Circuits that differ only in the starting vertex or the direction count as the same.

K4
H =
5.Hard
710983291ABCDEF

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =
6.Hard
1312582441513ABCDEFG

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 6; A itself is round 1.

start: Around 6
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G

Answer key

  1. 1. |E| = 8
  2. 2. |E| = 5
  3. 3. L = 8
  4. 4. H = 3
  5. 5. d(F) = 13
  6. 6. F

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