NMAK23004U Graphs and Groups

Volume 2023/2024

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject


This course covers a number of fundamental topics concerning groups of graph automorphisms, with an emphasis on group-theoretic notions and results.

Topics include:

1. Fundamentals of graph theory and of group theory

2. Graph automorphisms, transitive graphs

3. Group actions on graphs

4. Cayley graphs, Schreier graphs

5. Fundamental group of a graph, coverings

6. Free group: definition, elementary properties

7. Subgroups of free groups

8. Hanna Neumann conjecture

Learning Outcome

After completing the course, the student will have:

Knowledge about the subjects mentioned in the description of the content.

Skills to solve problems concerning the material covered.

The following Competences:

  • Have a good understanding of the fundamental concepts and results presented in lectures, including a thorough understanding of various proofs.
  • Establish connections between various concepts and results, and use the results discussed in lecture for various applications.
  • Be in control of the material discussed in the lectures to the extent of being able to solve problems concerning the material covered.
  • Be prepared to work with abstract concepts (from Graph Theory and Group Theory).
  • Handle complex problems concerning topics within the areas of Graph Theory and Group Theory.
Basic group theory and linear algebra, as covered by the courses LinAlg and Alg1 or equivalent.

Academic qualifications equivalent to a BSc degree is recommended.
5 hours of lectures and 4 hours of exercises per week for 7 weeks
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 130
  • Theory exercises
  • 28
  • Exam
  • 13
  • Total
  • 206
Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
Two written homework assignments and a final 3 hours in-class written exam. Each of the two written homework assignments counts 25% towards the final grade; the students will be given 5 days to work on each. The final 3 hours in-class written exam counts 50% towards the final grade, and it takes place in week 9.
Only certain aids allowed

All aids allowed for the two written homework assignments. The final 3 hours in-class written exam is without aids.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Exam period

Week 9 of Block 4


Oral examination, 30 minutes with 30 minutes preparation. For the preparation, written aids are allowed. 

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.