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
AABBCCDDEE0110010111110010100101110

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

|E| =
2.Easy

A tree has 27 vertices. How many edges |E| does it have?

|V| = 27
|E| =
3.Medium

A connected graph has 10 vertices and 12 edges. How many edges k must be removed to leave a spanning tree?

|V| = 10|E| = 12
k =
4.Medium
ABCDEEuler circuitEuler path, no circuitneither

Does the connected graph have an Euler circuit, an Euler path that is not a circuit, or neither? Click your answer.

|V| = 5|E| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
151416111312276ABCDEFG

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

|V| = 7|E| = 10
W =
6.Hard
ABCDE

How many walks of length 2 go from A 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| = 26
  3. 3. k = 3
  4. 4. Euler circuit
  5. 5. W = 38
  6. 6. N = 1

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