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

How many edges |E| does the complete bipartite graph K5,10 have?

K5,10
|E| =
2.Easy
AABBCCDDEEFF011000101110110010010011011101000110

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| = 9
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

How many different Hamilton circuits H does the complete graph K8 have? Circuits that differ only in the starting vertex or the direction count as the same.

K8
H =
5.Hard
6137812213121537ABCDEFG

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
6182111951778ABCDEFG

Prim’s algorithm builds a minimum spanning tree starting from vertex E. Click the edge it adds as edge number 2.

start: Ek = 2
  1. 1edge AC
  2. 2edge BC
  3. 3edge BD
  4. 4edge CE
  5. 5edge DF
  6. 6edge GB
  7. 7edge GC
  8. 8edge GD
  9. 9edge GE

Answer key

  1. 1. |E| = 50
  2. 2. |E| = 9
  3. 3. Euler path, no circuit
  4. 4. H = 2520
  5. 5. d(F) = 16
  6. 6. edge GB

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