Qraflar nəzəriyyəsiSyllabus

Subject code

İFS-31113yn

Credits

6

Student workload

180

Semester

Autumn semester

Academic year

2025-2026

Subject type

Elective

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a) 30 saat - mühazirə b) 30 saat seminar

Out-of-class hours

a) 72 saat - sərbəst iş b) 48 saat - hazırlıq

Qraflar nəzəriyyəsi fənni qrafların əsas anlayışlarını, növlərini və xassələrini, həmçinin onların müxtəlif sahələrdə tətbiqini öyrədir. fənn çərçivəsində qrafların izomorfizmi, marşrutlar, yollar, tsikllər, əlaqəli qraflar, ağaclar, eyler və hamilton qrafları, minimal örtən ağaclar, qrafın rənglənməsi, planar qraflar və şəbəkələrdə maksimal axın məsələləri, eləcə də prim, kraskal və falkerson alqoritmləri öyrənilir. kursun sonunda tələbələr qraf əsaslı məsələləri modelləşdirmək, müvafiq alqoritmləri tətbiq etmək və kompüter elmlərində, şəbəkə sistemlərində və optimallaşdırma problemlərində qraflar nəzəriyyəsindən səmərəli istifadə etmək bacarıqları əldə edirlər.

• lecture
• interactive discussion
• seminar
• presentations

1. 1

   CLO 1: Explains the basic concepts, types and methods of presentation of graphs.

2. 2

   CLO 2: It applies the concepts of route, path, cycle, connectivity, and distance to solving graph problems.

3. 3

   CLO 3: Solves problems on tree graphs, euler and hamilton graphs, uses prim and kraskal algorithms.

4. 4

   CLO 4: Analyzes graph coloring, planar graphs, and extremal graph problems.

5. 5

   CLO 5: It applies suitable graph algorithms in solving the maximal flow and optimal path problems.

6. 6

   CLO 6: It uses the methods of graph theory in computer science and network systems.

1. 1.
   Count. basic concepts of graph. methods of giving the graph. isomorphism of graphs. homeomorphic graphs.Lecture

   The concept of a graph, its vertex, tongue, degree and other basic elements are studied in the subject. representation of graphs by graphical representation, adjacency matrix, incidence matrix and list methods are explained. definition of isomorphic and homeomorphic graphs, their similarities and differences are also explored.

2. 2.
   Parts of the graph. subgraphs. partial counts (sugraffs). actions on graphs.Lecture

   In the topic, the concepts of parts of a graph, subgraph and partial graph are studied. the rules of construction of subgraphs and partial graphs, their main features are explained. join, intersection, complement and other basic operations on graphs are also studied.

3. 3.
   Routes. chains. cycles. roads. contours. finding the number of routes (paths) of a certain length in graphs.Lecture

   In the topic, the concepts of route, chain, path, cycle and contour are studied in graphs. the differences between these concepts and their role in examining graph connectivity are explained. also, finding the number of routes and paths of a certain length using the adjacency matrix is ​​investigated.

4. 4.
   Related graphs. strongly connected graphs. partitioning a graph into maximal strongly connected subgraphs.Lecture

   The concept of a connected graph and the condition of existence of a path between the vertices of the graph are studied in the topic. in directed graphs, the concept of strong connectivity and the property of reachability in both directions are explained. also, the partitioning of the graph into maximal strongly connected subgraphs and the determination of these subgraphs are investigated.

5. 5.
   Distance characteristics in graphs.Lecture

   In the subject, the concept of distance between two vertices in a graph and determination of the shortest path are studied. basic distance characteristics such as eccentricity, radius, diameter, and center of a graph are explained. also, the application of these characteristics in the analysis of the structure of the graph and the level of connectivity is investigated.

6. 6.
   Extremal problems in graphs and their solutions.Lecture

   In the subject, extreme optimization problems on graphs and their mathematical formulation are studied. basic properties of shortest path, minimal spanning tree, maximal flow, and similar problems are explained. algorithmic methods used to solve these problems and their fields of application are also investigated.

7. 7.
   Ordering vertices and edges of a directed graph by falkerson's algorithm. maximal path finding algorithm.Lecture

   In the topic, the rules for ordering vertices and edges of directed graphs based on falkerson's algorithm are studied. it explains how to define sequence relationships and place vertices on appropriate levels in a graph. algorithmic approaches used for finding the maximal path in a directed graph are also investigated.

8. 8.
   Tree graphs. problems of searching optimal tree graphs in weighted graphs. prim and kraskal algorithms.Lecture

   In the topic, the main concepts, properties of tree graphs and their role in the investigation of graph connectivity are studied. the problem of finding a minimal spanning tree in weighted graphs and its importance in terms of optimization are explained. also, the application of prim and kraskal algorithms for constructing an optimal tree is investigated.

9. 9.
   Giriş. dövlətəqədərki dövr və ibtidai insan münasibətlərinin formalaşması.Lecture

   Dövlətəqədərki dövrün əsas xüsusiyyətləri, ibtidai insan cəmiyyətinin yaranması və formalaşması, eyni zamanda qədim insanların həyat tərzi, əmək vərdişləri, ictimai münasibətlərin təşəkkülü, qəbilə və tayfa quruluşunun formalaşması, eləcə də dövlətin yaranmasına təsir edən sosial-iqtisadi proseslərdən bəhs edir.

   • • ftn4: tələbələrin ən azından minimum məlumat əldə etməsi, mövzular ətrafında öz fikrinin formalaşmasının səviyyəsi yoxlanılır.
   • • ftn3: tələbələrin bu və ya digər məsələlərlə bağlı obyektiv mövqeyini formalaşmasına nail olunur.
   • • ftn5: tələbələrə qədim tariximizin müasir dövrlə uzlaşdırılması vərdişləri aşılanır.
   • • ftn2: azərbaycan tarixi üzrə bəzi mübahisəli məsələlərə aydınlıq gətirilir.
   • • ftn1: azərbaycan tarixinin dövrlərinin əsas mahiyyəti izah edilir.
10. 10.
    Hamilton chain and cycle.Lecture

    In the topic, the concepts of hamiltonian chain and hamiltonian cycle are studied based on the principle of passing through all vertices of the graph only once. the differences between the hamiltonian chain and the hamiltonian cycle and how they differ from the euler chain and cycle are explained. also, basic approaches to determine the existence of a hamiltonian chain and cycle in a given graph are explored.

11. 11.
    Vector-cycles. basic cycles. fundamental system of cycles.Lecture

    In the subject, the expression of cycles in graphs in the form of vectors and their investigation through linear combinations are studied. the concept of basic cycles and the construction of all cycles of the graph based on this basis are explained. also, the finding of the fundamental system of cycles and its application in the analysis of the graph structure are investigated.

12. 12.
    Sets of independent and dominant vertices of a graph. graph kernel and its properties.Lecture

    In the topic, the set of independent vertices of a graph and the role of this set in the structure of the graph are studied. the concept of a set of dominant vertices and the coverage of all vertices of a graph by this set are explained. also, the core of the graph, its existence conditions and basic properties are investigated.

13. 13.
    Coloring graphs. the chromatic number of the graph.Lecture

    In the subject, the concept of coloring the vertices or edges of the graph based on certain rules is studied. the condition that neighboring vertices do not get the same color and the application of coloring in graph theory are explained. also, the chromatic number of the graph, its finding and its dependence on the structure of the graph are investigated.

14. 14.
    Planar graphs.Lecture

    Concepts of planar and planar graphs, their main features in graph theory are studied in the topic. the conditions for describing the graph's tongues on the plane without intersection are explained. the division of planar graphs into areas and their structural features are also investigated.

15. 15.
    Extreme flow issues in the network.Lecture

    In the subject, the concept of flow in the network, source, outlet, capacity and flow restrictions are studied. the mathematical formulation of the maximal flow problem and its role as an optimization problem in graph theory are explained. also, basic algorithmic approaches for finding extreme flow and the flow-cross-section relationship are explored.

1. A. namazov, r. amirova, "discrete mathematics", azerbaijan-2025
2. A.e. huseynov, m.i. seyidov, v.m. mammadov, "theory of graphs", azerbaijan-2018(opens in a new tab)