Topics in discrete mathematics 2

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M2
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

The lecturer chooses a few relevant topics in discrete mathematics, while paying attention to a possbile overlap with other courses in the program Mathematics (the overlap should be minimal) and prerequisites (those should be bound to obligatory courses of the programme Mathematics).

Readings

N. L. Biggs, A. T. White: Permutation Groups and Combinatorial Structures, Cambridge University Press, Cambridge, 1979.
C. Godsil, G. Royle: Algebraic Graph Theory. Springer, New York, 2001.
Jack H. van Lint, Robin J. Wilson: A Course in Combinatorics, Cambridge University Press, Cambridge, 2001.
Laszlo Lovasz, Jozsef Pelikan, Katalin Vesztergombi: Discrete Mathematics, Springer, Berlin-Heidelberg-New York, 2003.
Richard P. Stanley: Enumerative Combinatorics, Vol. 2, Cambridge University Press, New York-Cambridge, 1999.

Objectives and competences

Students becomes acquainted with the presented topics.

Intended learning outcomes

Knowledge and understanding: Student will understand the presented topics and results.
Application: Student will know how to use the new knowledge in different mathematical and other contexts.
Reflection: Student will be able to critically reflect the topic.
Transferable skills:. Skill of critical though, identification of discrete structures in nature and society.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

Homeworks or project
Written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Primož Potočnik:
POTOČNIK, Primož. Tetravalent arc-transitive locally-Klein graphs with long consistent cycles. European journal of combinatorics, ISSN 0195-6698, 2014, vol. 36, str. 270-281. [COBISS-SI-ID 16862041]
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. Cubic vertex-transitive graphs on up to 1280 vertices. Journal of symbolic computation, ISSN 0747-7171, 2013, vol. 50, str. 465-477. [COBISS-SI-ID 16520537]
POTOČNIK, Primož. Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2004, vol. 91, no. 2, str. 289-300. [COBISS-SI-ID 13087321]
Sandi Klavžar:
KLAVŽAR, Sandi. Structure of Fibonacci cubes: a survey. Journal of combinatorial optimization, ISSN 1382-6905, 2013, vol. 25, iss. 4, str. 505-522. [COBISS-SI-ID 16603737]
KLAVŽAR, Sandi, SHPECTOROV, Sergey. Convex excess in partial cubes. Journal of graph theory, ISSN 0364-9024, 2012, vol. 69, no. 4, str. 356-369. [COBISS-SI-ID 16243033]
HAMMACK, Richard H., IMRICH, Wilfried, KLAVŽAR, Sandi. Handbook of product graphs, (Discrete mathematics and its applications). Boca Raton, London, New York: CRC Press, cop. 2011. XVIII, 518 str., ilustr. ISBN 978-1-4398-1304-1. [COBISS-SI-ID 15916121]
Riste Škrekovski:
GOVORČIN, Jelena, KNOR, Martin, ŠKREKOVSKI, Riste. Line graph operation and small worlds. Information processing letters, ISSN 0020-0190. [Print ed.], 2013, vol. 113, iss. 5-6, str. 196-200. [COBISS-SI-ID 16561497]
DVOŘÁK, Zdeněk, LIDICKÝ, Bernard, ŠKREKOVSKI, Riste. Randić index and the diameter of a graph. European journal of combinatorics, ISSN 0195-6698, 2011, vol. 32, iss. 3, str. 434-442. [COBISS-SI-ID 17410905]
KAISER, Tomáš, STEHLÍK, Matěj, ŠKREKOVSKI, Riste. On the 2-resonance of fullerenes. SIAM journal on discrete mathematics, ISSN 0895-4801, 2011, vol. 25, no. 4, str. 1737-1745. [COBISS-SI-ID 16244569]