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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1.Easy

A tree has 22 vertices. How many edges |E| does it have?

|V| = 22
|E| =
2.Easy

A tree has 9 edges. How many vertices |V| does it have?

|E| = 9
|V| =
3.Medium

A connected graph has 17 vertices and 28 edges. How many edges k must be removed to leave a spanning tree?

|V| = 17|E| = 28
k =
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| = 10
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
9871398912ABCDEF

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
931112415311143ABCDEFG

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. |E| = 21
  2. 2. |V| = 10
  3. 3. k = 12
  4. 4. neither
  5. 5. d(D) = 22
  6. 6. d(F) = 8

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