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
ABCDEEuler 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| = 5|E| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 14 vertices and 19 edges. How many edges k must be removed to leave a spanning tree?

|V| = 14|E| = 19
k =
5.Hard
181731521652011ABCDEFG

Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 7|E| = 9
W =
6.Hard
1712187131581206ABCDEFG

Prim’s algorithm builds a minimum spanning tree starting from vertex G. Click the edge it adds as edge number 3.

start: Gk = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge EF
  8. 8edge GB
  9. 9edge GD
  10. 10edge GE

Answer key

  1. 1. A
  2. 2. B
  3. 3. Euler path, no circuit
  4. 4. k = 6
  5. 5. W = 53
  6. 6. edge BD

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