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 tree has 8 vertices. How many edges |E| does it have?

|V| = 8
|E| =
2.Easy

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

K5
|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| = 7
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A tree has 3 vertices of degree 4, 4 vertices of degree 5, 2 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 44 × deg 52 × deg 2
L =
5.Hard
ABCDEF

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

M = adjacency matrixL = 2
N =
6.Hard
2132014161819ABCDEF

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 5; skipped edges do not count.

k = 5
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge DF
  8. 8edge BE

Answer key

  1. 1. |E| = 7
  2. 2. |E| = 10
  3. 3. Euler path, no circuit
  4. 4. L = 20
  5. 5. N = 2
  6. 6. edge DF

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