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

A tree has 13 edges. How many vertices |V| does it have?

|E| = 13
|V| =
3.Medium

How many different Hamilton circuits H does the complete graph K5 have? Circuits that differ only in the starting vertex or the direction count as the same.

K5
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
4137134813151514ABCDEFG

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =
6.Hard
27131419117ABCDE

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

|V| = 5|E| = 7
W =

Answer key

  1. 1. C
  2. 2. |V| = 14
  3. 3. H = 12
  4. 4. Euler circuit
  5. 5. d(F) = 25
  6. 6. W = 24

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