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

How many edges |E| does the complete bipartite graph K6,11 have?

K6,11
|E| =
2.Easy
ABCDE

Exactly one vertex of the graph has degree 2. Click it.

deg = 2
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
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| = 8
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 17 vertices and 26 edges. How many edges k must be removed to leave a spanning tree?

|V| = 17|E| = 26
k =
5.Hard
15113613109ABCDE

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 3; skipped edges do not count.

k = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE
6.Hard
51420678182ABCDEF

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

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

Answer key

  1. 1. |E| = 66
  2. 2. D
  3. 3. neither
  4. 4. k = 10
  5. 5. edge BE
  6. 6. W = 35

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