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
AABBCCDD0011001011001000

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 4. Click it.

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

A connected graph has 18 vertices and 28 edges. How many edges k must be removed to leave a spanning tree?

|V| = 18|E| = 28
k =
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| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
6610114146213126ABCDEFG

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
  7. 7G
6.Hard
261516201713ABCDE

Prim’s algorithm builds a minimum spanning tree starting from vertex A. Click the edge it adds as edge number 3.

start: Ak = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE

Answer key

  1. 1. |E| = 3
  2. 2. B
  3. 3. k = 11
  4. 4. Euler path, no circuit
  5. 5. C
  6. 6. edge BE

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