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 7 vertices with degrees 4, 4, 3, 3, 2, 1, 1. How many edges |E| does it have?

deg: 4, 4, 3, 3, 2, 1, 1
|E| =
2.Easy

A forest (a graph without cycles) has 21 vertices and 5 connected components. How many edges |E| does it have?

|V| = 21c = 5
|E| =
3.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| = 8
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
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
8127125124412ABCDEF

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =
6.Hard
12105263197ABCDEF

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

|V| = 6|E| = 8
W =

Answer key

  1. 1. |E| = 9
  2. 2. |E| = 16
  3. 3. neither
  4. 4. H = 3
  5. 5. d(F) = 21
  6. 6. W = 27

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