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
ABCDEF

Exactly one vertex of the graph has degree 4. Click it.

deg = 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
2.Easy

A tree has 25 edges. How many vertices |V| does it have?

|E| = 25
|V| =
3.Medium

A connected graph has 6 vertices and 7 edges. How many edges k must be removed to leave a spanning tree?

|V| = 6|E| = 7
k =
4.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| = 12
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
11157665ABCDEF

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) =
6.Hard
ABCDEF

How many walks of length 3 go from D to B? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =

Answer key

  1. 1. B
  2. 2. |V| = 26
  3. 3. k = 2
  4. 4. Euler circuit
  5. 5. d(F) = 12
  6. 6. N = 5

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