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
AABBCCDDEE0110010010100010100100110

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

|E| =
2.Easy
AABBCCDDEE0010000110110010100000100

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

deg(D) =
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| = 9
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

How many different Hamilton circuits H does the complete graph K5 have? Circuits that differ only in the starting vertex or the direction count as the same.

K5
H =
5.Hard
421320171815126710ABCDEFG

Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 7|E| = 11
W =
6.Hard
126210125145ABCDEF

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. |E| = 5
  2. 2. deg(D) = 1
  3. 3. neither
  4. 4. H = 12
  5. 5. W = 44
  6. 6. d(F) = 23

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