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 K6,9 have?

K6,9
|E| =
2.Easy

A simple graph has 5 vertices with degrees 3, 3, 2, 1, 1. How many edges |E| does it have?

deg: 3, 3, 2, 1, 1
|E| =
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| = 12
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

How many different Hamilton circuits H does the complete graph K4 have? Circuits that differ only in the starting vertex or the direction count as the same.

K4
H =
5.Hard
182061412478ABCDEF

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

|V| = 6|E| = 8
W =
6.Hard
ABCDE

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

M = adjacency matrixL = 2
N =

Answer key

  1. 1. |E| = 54
  2. 2. |E| = 5
  3. 3. Euler circuit
  4. 4. H = 3
  5. 5. W = 49
  6. 6. N = 1

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