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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy

How many edges |E| does the complete bipartite graph K5,8 have?

K5,8
|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
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 K4 have? Circuits that differ only in the starting vertex or the direction count as the same.

K4
H =
5.Hard
7119137759ABCDEF

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
ABCDEF

How many walks of length 3 go from E to D? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =

Answer key

  1. 1. |E| = 40
  2. 2. B
  3. 3. neither
  4. 4. H = 3
  5. 5. d(F) = 15
  6. 6. N = 5

Full step-by-step solutions: practise this topic on examproblems.com.