#### Faculty of Technical Sciences

Subject: Fundamentals of Graph Theory and Combinatorics (17 - IFE212)

Basic Information

 Category Scientific-professional Scientific or art field: Teorijska i primenjena matematika Interdisciplinary yes ECTS 7
Native organizations units

 Department of Fundamentals Sciences Chair of Mathematics
Course specification

Course is active from 15.11.2012..

Precondition courses

Course idMandatoryMandatory
AlgebraYesYes
The main aim of the course is to train students abstract thinking and acquire basic knowledge in the field of classical combinatorial objects, non-classical combinatorial objects and graph theory. Students will learn to classify combinatorial problems and solve them using well-known combinatorial methods, through the acquisition of theoretical knowledge and solving practical examples. Through the learning of well-known concepts and theorems from graph theory, students will be able to set graphic formal models from other fields (e.g. computer science and transport engineering). Properties of graphs will be precisely mathematically proved, with the aim of further development of students skills for deriving proofs.
As outcome of the course, students will acquire basic knowledge in the field of classical combinatorial objects, non-classical combinatorial objects and graph theory, with their abstract thinking and the skills of proofing being greatly improved. Students will be able to recognize combinatorial objects and solve them by known methods, as well as to develop and analyse graph models in some other fields.
Lectures (Theoretical lectures). Logic relations, classical combinatorial objects (permutations, variations and combinations with and without repetition), partition sets, Stirling numbers, combinatorics on words, recurrent formulas, generative functions, basic concepts of graph theory, connection graphs, special classes of graphs, isomorphism of graphs, matrices neighborhoods, operations on graphs, trees, planar graphs (the fundamental theorem), Euler and Hamiltonian paths, Hamiltonian contours. Practice lectures (lab): In laboratory exercises adequate examples and tests from the theoretical lectures are done in order to exercise lectured theory where exercises contribute to understanding of the theory.
Lectures; Computing practice. Consultations. Lectures are dynamic and interactive. In lectures theoretical part of the course is presented accompanied by characteristic and representative examples in order to better understand the matter. In practice, which follows lectures, typical problems are solved and lectured theory is deepened. Besides lectures and practice, regular consultations and group consultations are also held. Part of the course, which is a logical unit, can be passed within the teaching process in the following 2 modules. The first module: Combinatorics. The second module: Graph theory.
AuthorsNameYearPublisherLanguage
Doroslovački, R.Kombinatorika na rečima2000Feljton, Novi SadSerbian language
Tošić RatkoKombinatorika1999Univezitet u Novom SaduSerbian language
Robin J. WilsonIntroduction to Graph Theory1996Robin WilsonEnglish
I. Bošnjak, D. Mašulović, V. Petrović, R. TošićZbirka zadataka iz teorije grafova2006Univerzitet u Novom Sadu, Novi SadSerbian language
D.Mašulović, M.PechZbirka zadataka iz kombinatorike2015Prirodno-matematički fakultet, Departman za matematiku i informatikuSerbian language
Course activity Pre-examination ObligationsNumber of points
TestYesYes10.00
TestYesYes10.00
Written part of the exam - tasks and theoryNoYes30.00
Lecture attendanceYesYes5.00
Computer exercise attendanceYesYes5.00
Theoretical part of the examNoYes40.00
Name and surnameForm of classes

Lectures

#### Duraković NatašaAssistant Professor

Practical classes