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

A simple graph has 7 vertices with degrees 4, 4, 4, 3, 2, 2, 1. How many edges |E| does it have?

deg: 4, 4, 4, 3, 2, 2, 1
|E| =
2.Easy
AABBCCDD0111101011011010

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

|E| =
3.Medium
ABCDEFEuler 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| = 6|E| = 7
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.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 =
5.Hard
66714335ABCDEF

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
2053191213107142ABCDEFG

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 6; skipped edges do not count.

k = 6
  1. 1edge AB
  2. 2edge AC
  3. 3edge BD
  4. 4edge DE
  5. 5edge DF
  6. 6edge EF
  7. 7edge GB
  8. 8edge GC
  9. 9edge GD
  10. 10edge GE

Answer key

  1. 1. |E| = 10
  2. 2. |E| = 5
  3. 3. neither
  4. 4. H = 360
  5. 5. d(F) = 14
  6. 6. edge DF

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