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
ABCDEF

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
2.Easy

A simple graph has 7 vertices with degrees 4, 4, 3, 3, 2, 2, 2. How many edges |E| does it have?

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

How many different Hamilton circuits H does the complete graph K5 have? Circuits that differ only in the starting vertex or the direction count as the same.

K5
H =
4.Medium
ABCDEFGEuler circuitEuler path, no circuitneither

Does the connected graph have an Euler circuit, an Euler path that is not a circuit, or neither? Click your answer.

|V| = 7|E| = 11
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
1111296101441ABCDEFG

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

start: Aend: D
d(D) =
6.Hard
1281112111381010ABCDEFG

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) =

Answer key

  1. 1. C
  2. 2. |E| = 10
  3. 3. H = 12
  4. 4. Euler path, no circuit
  5. 5. d(D) = 19
  6. 6. d(F) = 30

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