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 7 vertices with degrees 3, 3, 2, 2, 2, 1, 1. How many edges |E| does it have?

deg: 3, 3, 2, 2, 2, 1, 1
|E| =
2.Easy

A simple graph has 7 vertices with degrees 4, 3, 2, 2, 1, 1, 1. How many edges |E| does it have?

deg: 4, 3, 2, 2, 1, 1, 1
|E| =
3.Medium
ABCDEFEuler 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| = 6|E| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 13 vertices and 20 edges. How many edges k must be removed to leave a spanning tree?

|V| = 13|E| = 20
k =
5.Hard
82920193113ABCDEF

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

|V| = 6|E| = 8
W =
6.Hard
4213910151231811ABCDEFG

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 4; skipped edges do not count.

k = 4
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge GB
  9. 9edge GC
  10. 10edge GD

Answer key

  1. 1. |E| = 7
  2. 2. |E| = 7
  3. 3. Euler circuit
  4. 4. k = 8
  5. 5. W = 27
  6. 6. edge BD

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