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
AABBCCDD0101101001001000

The adjacency matrix of a simple undirected graph is shown. Find the degree deg(B) of vertex B.

deg(B) =
2.Easy

A simple graph has 7 vertices with degrees 4, 3, 3, 3, 2, 2, 1. How many edges |E| does it have?

deg: 4, 3, 3, 3, 2, 2, 1
|E| =
3.Medium
ABCDEFEuler 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| = 6|E| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 13 vertices and 16 edges. How many edges k must be removed to leave a spanning tree?

|V| = 13|E| = 16
k =
5.Hard
1716476101319128ABCDEFG

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 4; skipped edges do not count.

k = 4
  1. 1edge AB
  2. 2edge AC
  3. 3edge BD
  4. 4edge DE
  5. 5edge DF
  6. 6edge EF
  7. 7edge GB
  8. 8edge GC
  9. 9edge GD
  10. 10edge GE
6.Hard
71274216123ABCDEFG

Use Dijkstra’s algorithm to find the length d(D) of the shortest path from A to D in the weighted graph.

start: Aend: D
d(D) =

Answer key

  1. 1. deg(B) = 2
  2. 2. |E| = 9
  3. 3. neither
  4. 4. k = 4
  5. 5. edge GE
  6. 6. d(D) = 14

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