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
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
2.Easy
AABBCCDD0001001001011010

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

|E| =
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| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 12 vertices and 15 edges. How many edges k must be removed to leave a spanning tree?

|V| = 12|E| = 15
k =
5.Hard
121012159615ABCDEF

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
71571413615111ABCDEFG

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) =

Answer key

  1. 1. A
  2. 2. |E| = 3
  3. 3. Euler path, no circuit
  4. 4. k = 4
  5. 5. B
  6. 6. d(F) = 45

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