| CODE | MAT3410 | ||||||||
| TITLE | Graph Theory | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 5 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | - Definitions and elementary results on graphs; - Graphical degree sequences; - Spectral properties of Bipartite Graphs; - Spectral Decomposition; - Spectral Moments; - The Bose-Mesner Algebra of the Adjacency Matrix; - The Rayleigh Quotient and the eigenvalue bounds; - Cages and Moore Graphs; - Planar graphs and Platonic Solids; - Walks; - Distance regular graphs, Intersection Arrays and strongly regular graphs;- The Laplacian and the Matrix Tree Theorem; - Cayleys theorem on the number of spanning trees, - Cographs, Cotrees and Threshold graphs; - Vector spaces associated with graphs; - Cycle-cutset duality; Vertex and edge graph colourings: - The Chromatic Polynomial and Moebius Inversion. Main Texts: - Biggs N.L; Algebraic, Cambridge University Press, 1996/2011. - Wilson R.J., Introduction to Graph Theory, Longman, 4th Edition, 1996. - West D.B., Introduction to Graph Theory, Prentice Hall, 2nd Edition, 2001. - Biggs N.L., Discrete Mathematics, Oxford Science Publications, Clarendon Press, 1989. - Agnarsson G. and Greenlaw R., Graph Theory: Modelling, Applications and Algorithms, Pearson, 2006. - Gross J.L. and Yellen J., Handbook of Graph Theory, CRC Press, 2nd Edition, 2004. Supplementary Reading - Diestel R., Graph Theory, Springer-Verlag, 3rd Edition, 2006. - Cameron P.J., Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1994. - Bryant V., Aspects of Combinatorics: A Wide Ranging Introduction, Cambridge University Press, Cambridge, 1993. |
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| ADDITIONAL NOTES | Follows from: MAT3114, MAT3425 Leads to: MAT5414 |
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| STUDY-UNIT TYPE | Lecture | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Irene Sciriha Aquilina |
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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 Units not attracting a sufficient number of registrations may be withdrawn without notice.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 2023/4. It may be subject to change in subsequent years. |
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