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
AABBCCDDEEFF011000100010100000000011010101000110

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

deg(E) =
2.Easy
ABCDEF

Exactly one vertex of the graph has degree 4. Click it.

deg = 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
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

A connected graph has 19 vertices and 19 edges. How many edges k must be removed to leave a spanning tree?

|V| = 19|E| = 19
k =
5.Hard
ABCDE

How many closed walks of length 2 start and end at E? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =
6.Hard
2111274151413ABCDEFG

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
  7. 7G

Answer key

  1. 1. deg(E) = 3
  2. 2. B
  3. 3. neither
  4. 4. k = 1
  5. 5. N = 3
  6. 6. G

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