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

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

|V| = 6
Σ deg =
2.Easy

A forest (a graph without cycles) has 8 vertices and 6 connected components. How many edges |E| does it have?

|V| = 8c = 6
|E| =
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| = 9
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

How many different Hamilton circuits H does the complete graph K8 have? Circuits that differ only in the starting vertex or the direction count as the same.

K8
H =
5.Hard
7145318112017ABCDEF

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

|V| = 6|E| = 8
W =
6.Hard
9151478414415ABCDEFG

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

start: Aend: E
d(E) =

Answer key

  1. 1. Σ deg = 12
  2. 2. |E| = 2
  3. 3. Euler path, no circuit
  4. 4. H = 2520
  5. 5. W = 43
  6. 6. d(E) = 23

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