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
AABBCCDDEEFF001000001100110010010011001100000100

The adjacency matrix of a simple undirected graph is shown. Find the degree deg(A) of vertex A.

deg(A) =
2.Easy

A simple graph has 6 vertices with degrees 4, 4, 3, 3, 2, 2. How many edges |E| does it have?

deg: 4, 4, 3, 3, 2, 2
|E| =
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
ABCDEFEuler 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| = 6|E| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
13163291412ABCDE

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

|V| = 5|E| = 7
W =
6.Hard
146456101515101513ABCDEFG

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 5; A itself is round 1.

start: Around 5
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G

Answer key

  1. 1. deg(A) = 1
  2. 2. |E| = 9
  3. 3. H = 12
  4. 4. Euler path, no circuit
  5. 5. W = 27
  6. 6. D

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