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 27 vertices. How many edges |E| does it have?

|V| = 27
|E| =
2.Easy

A tree has 10 edges. How many vertices |V| does it have?

|E| = 10
|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| = 10
  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
15161891343ABCDE

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

start: Bk = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE
6.Hard
ABCDE

How many walks of length 2 go from E to B? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =

Answer key

  1. 1. |E| = 26
  2. 2. |V| = 11
  3. 3. Euler path, no circuit
  4. 4. H = 60
  5. 5. edge CE
  6. 6. N = 2

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