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
AABBCCDDEEFF011000100010100010000001011001000110

The adjacency matrix of a simple undirected graph is shown. How many edges |E| does the graph have?

|E| =
2.Easy
ABCDE

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

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
3.Medium

How many different Hamilton circuits H does the complete graph K7 have? Circuits that differ only in the starting vertex or the direction count as the same.

K7
H =
4.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
5.Hard
1513121312591211ABCDEFG

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
129153122910ABCDEF

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

Answer key

  1. 1. |E| = 6
  2. 2. D
  3. 3. H = 360
  4. 4. neither
  5. 5. d(F) = 21
  6. 6. E

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