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
ABCDEFG

Exactly one vertex of the graph has degree 2. Click it.

deg = 2
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
2.Easy
ABCDEFG

Exactly one vertex of the graph has degree 4. Click it.

deg = 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
3.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| = 7
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.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 =
5.Hard
91181396210137ABCDEFG

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
761264111151ABCDEFG

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) =

Answer key

  1. 1. F
  2. 2. B
  3. 3. neither
  4. 4. H = 12
  5. 5. d(F) = 24
  6. 6. d(D) = 16

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