Module code: MAT3043

Module Overview

Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well developed applications to a wide range of other disciplines (including operations research, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.

Module provider


Module Leader

SKELDON Anne (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

Module cap (Maximum number of students): N/A

Overall student workload

Independent Learning Hours: 117

Lecture Hours: 33

Module Availability

Semester 2

Prerequisites / Co-requisites


Module content

Indicative content includes:

  1. The language of graph theory;

  2. Elementary results on paths, cycles, trees, cut-sets, Hamiltonian and Eulerian graphs;

  3. Examples from enumerative theory, including Cayley’s theorem on trees;

  4. Graphs embedded in surfaces; the genus of a graph;

  5. Spectral methods: the adjacency and Laplacian matrices;

  6. Graph polynomials, colourings and Ising / Potts models;

  7. Network route and flow optimisation problems;

  8. Applications to Markov chains and decision processes;

  9. Introduction to flux balance and related methods in systems biology;

  10. Examples and properties of small world and scale free networks.       


Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test IN-SEMESTER TEST (50 MINS) 20
Examination EXAMINATION 80

Alternative Assessment


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

That they have learned the basic material in the field, and are able to apply it to examples and problems.


Thus, the summative assessment for this module consists of:

  • In-semester test. Constitutes 20% of the final mark.

  • Final Examination, 2 hours, end of Semester. Constitutes 80% of final mark.


    Formative assessment and feedback

Students will receive verbal feedback in tutorials. There will also be unassessed coursework on which students will receive written feedback


Module aims

  • This module aims to provide an introduction to graph theory, motivated and illustrated by applications to the life, physical and social sciences and to business.  

Learning outcomes

Attributes Developed
1 Demonstrate understanding of the language and proof techniques used in elementary graph theory KC
2 Apply methods from combinatorics, linear algebra and topology to graphs KCT
3 Apply graph theoretical methods and techniques to network optimisation problems;  CT
4 Demonstrate an elementary knowledge of a range of applications of graph theory to the life, physical and social sciences and to business.  CPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Equip students with the knowledge, practical experience and confidence to apply the techniques of Graph Theory to abstract and practical problems.


The learning and teaching methods include:

3 hours of lectures and tutorials per week for 11 weeks. Learning takes place through lectures, tutorials, exercises, coursework, tests and background reading.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list
Upon accessing the reading list, please search for the module using the module code: MAT3043

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2020/1 academic year.