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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy

How many edges |E| does the complete bipartite graph K6,6 have?

K6,6
|E| =
2.Easy

A simple graph has 7 vertices with degrees 4, 4, 3, 3, 2, 2, 2. How many edges |E| does it have?

deg: 4, 4, 3, 3, 2, 2, 2
|E| =
3.Medium

A connected graph has 11 vertices and 18 edges. How many edges k must be removed to leave a spanning tree?

|V| = 11|E| = 18
k =
4.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| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
71012510961ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 4; A itself is round 1.

start: Around 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
6.Hard
20113119871817ABCDEFG

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

|V| = 7|E| = 9
W =

Answer key

  1. 1. |E| = 36
  2. 2. |E| = 10
  3. 3. k = 8
  4. 4. Euler circuit
  5. 5. C
  6. 6. W = 57

Full step-by-step solutions: practise this topic on examproblems.com.