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 3, 3, 2, 2, 2. How many edges |E| does it have?

deg: 3, 3, 2, 2, 2
|E| =
2.Easy
ABCDEF

Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
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 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 =
5.Hard
511746658ABCDEF

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
6.Hard
179613431914ABCDEF

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 3; skipped edges do not count.

k = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge EF
  8. 8edge BE

Answer key

  1. 1. |E| = 6
  2. 2. D
  3. 3. H = 12
  4. 4. L = 8
  5. 5. C
  6. 6. edge BC

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