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
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
2.Easy

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

deg: 3, 3, 2, 1, 1
|E| =
3.Medium

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

4 × deg 32 × deg 42 × deg 5
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
154710613510ABCDEF

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
12167201581814ABCDEF

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

|V| = 6|E| = 8
W =

Answer key

  1. 1. C
  2. 2. |E| = 5
  3. 3. L = 16
  4. 4. H = 60
  5. 5. d(F) = 16
  6. 6. W = 59

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