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 K2,6 have?

K2,6
|E| =
2.Easy
ABCDE

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 5
Σ deg =
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| = 10
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 15 vertices and 26 edges. How many edges k must be removed to leave a spanning tree?

|V| = 15|E| = 26
k =
5.Hard
2631110615102ABCDEF

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
26103241215ABCDEF

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) =

Answer key

  1. 1. |E| = 12
  2. 2. Σ deg = 10
  3. 3. Euler path, no circuit
  4. 4. k = 12
  5. 5. C
  6. 6. d(F) = 15

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