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 4, 3, 3, 2, 2. How many edges |E| does it have?

deg: 4, 3, 3, 2, 2
|E| =
2.Easy
ABCDEF

Exactly one vertex of the graph has degree 3. Click it.

deg = 3
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
3.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 =
4.Medium

A connected graph has 10 vertices and 11 edges. How many edges k must be removed to leave a spanning tree?

|V| = 10|E| = 11
k =
5.Hard
ABCDE

How many walks of length 2 go from B to A? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =
6.Hard
ABCDEF

How many walks of length 2 go from C to E? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =

Answer key

  1. 1. |E| = 7
  2. 2. E
  3. 3. H = 60
  4. 4. k = 2
  5. 5. N = 1
  6. 6. N = 1

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