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
ABCDE

Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
2.Easy

How many edges |E| does the complete bipartite graph K3,7 have?

K3,7
|E| =
3.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| = 5
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A tree has 3 vertices of degree 3, 4 vertices of degree 4, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 34 × deg 4
L =
5.Hard
111111441515415ABCDEFG

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
ABCDEF

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

M = adjacency matrixL = 2
N =

Answer key

  1. 1. A
  2. 2. |E| = 21
  3. 3. Euler circuit
  4. 4. L = 13
  5. 5. d(F) = 30
  6. 6. N = 1

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