Qraflar nəzəriyyəsiTopics

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.