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
AABBCCDDEEFF010000101100010000010010000101000010

The adjacency matrix of a simple undirected graph is shown. How many edges |E| does the graph have?

|E| =
3.Medium

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

3 × deg 5
L =
4.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 =
5.Hard
10111156511813ABCDEFG

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
615473181613ABCDEF

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 4; skipped edges do not count.

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

Answer key

  1. 1. G
  2. 2. |E| = 5
  3. 3. L = 11
  4. 4. H = 3
  5. 5. B
  6. 6. edge BD

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