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 5-regular graph has 12 vertices (every vertex has degree 5). How many edges |E| does it have?

n = 12k = 5
|E| =
2.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
3.Medium

A connected graph has 11 vertices and 11 edges. How many edges k must be removed to leave a spanning tree?

|V| = 11|E| = 11
k =
4.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 =
5.Hard
1716420527ABCDE

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

|V| = 5|E| = 7
W =
6.Hard
ABCDE

How many walks of length 3 go from A to E? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =

Answer key

  1. 1. |E| = 30
  2. 2. G
  3. 3. k = 1
  4. 4. H = 12
  5. 5. W = 27
  6. 6. N = 2

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