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.

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Name: ____________________   Date: ____________

1.Easy

A simple graph has 5 vertices with degrees 4, 3, 2, 2, 1. How many edges |E| does it have?

deg: 4, 3, 2, 2, 1
|E| =
2.Easy

A tree has 12 vertices. How many edges |E| does it have?

|V| = 12
|E| =
3.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 =
4.Medium

A tree has 3 vertices of degree 3, 4 vertices of degree 4, 3 vertices of degree 5, 4 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 34 × deg 43 × deg 54 × deg 2
L =
5.Hard
315113159683ABCDEFG

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) =
6.Hard
7101171239ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 3; A itself is round 1.

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

Answer key

  1. 1. |E| = 6
  2. 2. |E| = 11
  3. 3. H = 2520
  4. 4. L = 22
  5. 5. d(F) = 23
  6. 6. D

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