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 graph K7 have?

K7
|E| =
2.Easy

A 2-regular graph has 8 vertices (every vertex has degree 2). How many edges |E| does it have?

n = 8k = 2
|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

A connected graph has 10 vertices and 21 edges. How many edges k must be removed to leave a spanning tree?

|V| = 10|E| = 21
k =
5.Hard
111215144111511213ABCDEFG

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
  7. 7G
6.Hard
37164201418ABCDE

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 4; skipped edges do not count.

k = 4
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE

Answer key

  1. 1. |E| = 21
  2. 2. |E| = 8
  3. 3. H = 60
  4. 4. k = 12
  5. 5. G
  6. 6. edge DE

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