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
ABCDE

Exactly one vertex of the graph has degree 3. Click it.

deg = 3
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
2.Easy
ABCDEFG

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 7
Σ deg =
3.Medium

How many different Hamilton circuits H does the complete graph K6 have? Circuits that differ only in the starting vertex or the direction count as the same.

K6
H =
4.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| = 5
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
71554162317ABCDEF

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 5; skipped edges do not count.

k = 5
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge DF
  8. 8edge EF
6.Hard
13213610738ABCDEF

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. E
  2. 2. Σ deg = 16
  3. 3. H = 60
  4. 4. Euler circuit
  5. 5. edge AB
  6. 6. d(D) = 18

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