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
AABBCCDD0111101011011010

The adjacency matrix of a simple undirected graph is shown. Find the degree deg(D) of vertex D.

deg(D) =
2.Easy

A tree has 20 edges. How many vertices |V| does it have?

|E| = 20
|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 K8 have? Circuits that differ only in the starting vertex or the direction count as the same.

K8
H =
5.Hard
4112151266ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 3; A itself is round 1.

start: Around 3
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
6.Hard
13137531169ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 4; A itself is round 1.

start: Around 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F

Answer key

  1. 1. deg(D) = 2
  2. 2. |V| = 21
  3. 3. neither
  4. 4. H = 2520
  5. 5. B
  6. 6. D

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