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

How many edges |E| does the complete bipartite graph K5,8 have?

K5,8
|E| =
2.Easy
ABCDEFG

Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
3.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
4.Medium

A connected graph has 13 vertices and 18 edges. How many edges k must be removed to leave a spanning tree?

|V| = 13|E| = 18
k =
5.Hard
451415101912206ABCDEFG

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

|V| = 7|E| = 9
W =
6.Hard
ABCDE

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

M = adjacency matrixL = 2
N =

Answer key

  1. 1. |E| = 40
  2. 2. A
  3. 3. Euler path, no circuit
  4. 4. k = 6
  5. 5. W = 52
  6. 6. N = 2

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