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
ABCDEF

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
2.Easy

A tree has 35 vertices. How many edges |E| does it have?

|V| = 35
|E| =
3.Medium

How many different Hamilton circuits H does the complete graph K5 have? Circuits that differ only in the starting vertex or the direction count as the same.

K5
H =
4.Medium

A tree has 4 vertices of degree 3, 4 vertices of degree 4, 3 vertices of degree 5, and all its other vertices are leaves (degree 1). How many leaves L does it have?

4 × deg 34 × deg 43 × deg 5
L =
5.Hard
798162014113ABCDEF

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

|V| = 6|E| = 8
W =
6.Hard
13155715101112ABCDEF

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
  2. 2. |E| = 34
  3. 3. H = 12
  4. 4. L = 23
  5. 5. W = 43
  6. 6. d(F) = 28

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