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

A tree has 13 vertices. How many edges |E| does it have?

|V| = 13
|E| =
2.Easy
AABBCCDD0111100010011010

The adjacency matrix of a simple undirected graph is shown. How many edges |E| does the graph have?

|E| =
3.Medium

A tree has 2 vertices of degree 3, 2 vertices of degree 4, 4 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

2 × deg 32 × deg 44 × deg 2
L =
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| = 10
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
ABCDE

How many walks of length 2 go from C to D? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =
6.Hard
11966146159ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 3; A itself is round 1.

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

Answer key

  1. 1. |E| = 12
  2. 2. |E| = 4
  3. 3. L = 8
  4. 4. neither
  5. 5. N = 2
  6. 6. E

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