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
ABCDEF

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 6
Σ deg =
2.Easy

A tree has 9 edges. How many vertices |V| does it have?

|E| = 9
|V| =
3.Medium

How many different Hamilton circuits H does the complete graph K4 have? Circuits that differ only in the starting vertex or the direction count as the same.

K4
H =
4.Medium

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

4 × deg 4
L =
5.Hard
915997111189ABCDEFG

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
84294128104ABCDEF

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. Σ deg = 12
  2. 2. |V| = 10
  3. 3. H = 3
  4. 4. L = 10
  5. 5. D
  6. 6. d(F) = 18

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