| CODE | MAT5413 | ||||||||
| TITLE | Algebraic Graph Theory: Graphs, Groups and Reconstruction | ||||||||
| UM LEVEL | 05 - Postgraduate Modular Diploma or Degree Course | ||||||||
| MQF LEVEL | 7 | ||||||||
| ECTS CREDITS | 15 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | Graphs and groups: Isomorphisms, vertex-, edge- and arc-transitivity, semisymmetric graphs; Cayley colour graphs: Cayley graphs; The automorphism group and the spectrum: Graphical regular representations and pseudosimilarity; Introduction to strongly regular graphs, stability of graphs; The reconstruction problem: Introduction, the edge and the vertex problems, Kelly's lemma and its converse; Regular graphs, disconnected graphs, maximal planar graphs; Reconstruction numbers; Counting arguments in reconstruction. Study-unit Aims: To expose the student to the main results, methods and ideas in algebraic graph theory; To provide the student with the necessary basic tools and training for doing independent research in some topics related mostly with graph symmetries. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Analyse concepts related with groups and graphs; - Recognise the nature of the graph isomorphism problem, especially in relation to the reconstruction problem; - Apply counting arguments in reconstruction. 2. Skills: By the end of the study-unit the student will be able to: - Formulate and investigate original problems in the field; - Apply methods and ideas covered in the study-unit to obtain new results; - Write mathematical material confidently, accurately and efficiently, making good use of algebraic graph theory. Main Text/s and any supplementary readings: Lauri J. and Scapellato R., "Topics in Graph Automorphisms and Reconstruction", Cambridge University Press, 2003. Biggs N. L., "Algebraic Graph Theory", Cambridge University Press, 2nd Edition, 1994. |
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| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||||
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years. |
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