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
ABCDE

Exactly one vertex of the graph has degree 3. Click it.

deg = 3
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
2.Easy
ABCDEF

Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
3.Medium

A connected graph has 19 vertices and 20 edges. How many edges k must be removed to leave a spanning tree?

|V| = 19|E| = 20
k =
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
410515319168ABCDEF

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

|V| = 6|E| = 8
W =
6.Hard
8144131014515ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 4; A itself is round 1.

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

Answer key

  1. 1. B
  2. 2. F
  3. 3. k = 2
  4. 4. H = 2520
  5. 5. W = 38
  6. 6. D

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