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

How many edges |E| does the complete bipartite graph K4,12 have?

K4,12
|E| =
2.Easy

A tree has 18 edges. How many vertices |V| does it have?

|E| = 18
|V| =
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 K6 have? Circuits that differ only in the starting vertex or the direction count as the same.

K6
H =
5.Hard
ABCDE

How many walks of length 3 go from E to D? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =
6.Hard
1614204181110ABCDEF

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 3; skipped edges do not count.

k = 3
  1. 1edge AC
  2. 2edge BC
  3. 3edge BD
  4. 4edge CE
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge BE

Answer key

  1. 1. |E| = 48
  2. 2. |V| = 19
  3. 3. Euler path, no circuit
  4. 4. H = 60
  5. 5. N = 4
  6. 6. edge DF

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