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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1.Easy

How many edges |E| does the complete bipartite graph K5,7 have?

K5,7
|E| =
2.Easy

A 2-regular graph has 7 vertices (every vertex has degree 2). How many edges |E| does it have?

n = 7k = 2
|E| =
3.Medium
ABCDEFGEuler 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| = 7|E| = 12
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 7 vertices and 7 edges. How many edges k must be removed to leave a spanning tree?

|V| = 7|E| = 7
k =
5.Hard
106910148312ABCDEF

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
ABCDE

How many closed walks of length 2 start and end at B? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =

Answer key

  1. 1. |E| = 35
  2. 2. |E| = 7
  3. 3. Euler circuit
  4. 4. k = 1
  5. 5. d(F) = 13
  6. 6. N = 3

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