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

A tree has 34 vertices. How many edges |E| does it have?

|V| = 34
|E| =
2.Easy

A 5-regular graph has 10 vertices (every vertex has degree 5). How many edges |E| does it have?

n = 10k = 5
|E| =
3.Medium

How many different Hamilton circuits H does the complete graph K6 have? Circuits that differ only in the starting vertex or the direction count as the same.

K6
H =
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
ABCDE

How many closed walks of length 3 start and end at C? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =
6.Hard
3211797145ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 5; A itself is round 1.

start: Around 5
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F

Answer key

  1. 1. |E| = 33
  2. 2. |E| = 25
  3. 3. H = 60
  4. 4. H = 360
  5. 5. N = 2
  6. 6. D

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