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 2-regular graph has 7 vertices (every vertex has degree 2). How many edges |E| does it have?

n = 7k = 2
|E| =
2.Easy
ABCDEFG

Exactly one vertex of the graph has degree 4. Click it.

deg = 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
3.Medium

A tree has 3 vertices of degree 4, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 4
L =
4.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 =
5.Hard
171512205612ABCDEF

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

|V| = 6|E| = 8
W =
6.Hard
85910151199510ABCDEFG

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) =

Answer key

  1. 1. |E| = 7
  2. 2. B
  3. 3. L = 8
  4. 4. H = 60
  5. 5. W = 31
  6. 6. d(F) = 27

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