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
AABBCCDDEEFF011000101010110000000011010101000110

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

deg(D) =
2.Easy

A 4-regular graph has 11 vertices (every vertex has degree 4). How many edges |E| does it have?

n = 11k = 4
|E| =
3.Medium

A tree has 3 vertices of degree 3, 4 vertices of degree 5, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 34 × deg 5
L =
4.Medium

A connected graph has 10 vertices and 18 edges. How many edges k must be removed to leave a spanning tree?

|V| = 10|E| = 18
k =
5.Hard
7821011141210111314ABCDEFG

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
811491011514ABCDEF

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

Answer key

  1. 1. deg(D) = 2
  2. 2. |E| = 22
  3. 3. L = 17
  4. 4. k = 9
  5. 5. d(F) = 29
  6. 6. E

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