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# Lectures on the theory of graphs. You can use both teachers and students.

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Uploaded:

**11.01.2006**

Content: 60111123833490.zip (171,82 kB)

# Description

Lectures on the theory of graphs can be used by teachers to give lectures and students for the exam.

Doc file is easily converted into a spur.

Contents:

Basic concepts of graph theory.

Problems in the theory of graphs.

Basic definitions.

Valence.

Isomorphism of graphs.

Matrix ways to specify graphs and operations on them.

Matrix method of specifying the graph.

Basic operations on graphs.

Combining graphs.

Routes in graphs.

The concept of the route.

Routes in directed graphs.

Connectivity in graphs.

Connectedness and adjacency matrix of the graph.

Matrix vzaimodostizhimosti.

Trees.

Free trees.

Oriented, ordered and binary trees.

Euler and Hamiltonian graphs.

The problem of the bridges of Koenigsberg.

An algorithm for constructing Euler Euler cycle in the graph.

Hamiltonian graphs.

Estimating the number of Euler and Hamiltonian graphs

The fundamental cycles and cuts.

Fundamental cycles.

Incisions.

Planarity and coloring of graphs.

Planar graphs.

The coloring of graphs.

Algorithms coloring.

Communication theory of graphs with binary relations and vector spaces.

Relationship on the sets and graphs.

Vector spaces associated with graphs.

The shortest route in the graph.

Distances in graphs.

Bellman-Ford algorithm.

Coatings and independence.

Covers a multitude of vertices and edges.

Independent set of vertices and edges.

Dominating set.

The traveling salesman problem.

Statement of the Problem

Detours of vertices of depth and width.

The decision of the traveling salesman problem.

Flows in networks.

Basic definitions.

The theorem of Ford and Fulkerson.

An algorithm for constructing the maximum flow.

Network planning and management.

Elements of the network schedule.

Time parameters of the network schedule.

The distribution of limited resources.

An analysis of technical systems (for example, an electrical circuit).

Kirchhoff's law.

Basic equations.

Signal graphs.

General understanding of the signaling columns.

Conversion of signal graphs.

# Additional information

Lectures on the theory of graphs can be used by teachers to give lectures and students for the exam.

Contents:

Basic concepts of graph theory.

Problems in the theory of graphs.

Basic definitions.

Valence.

Isomorphism of graphs.

Matrix ways to specify graphs and operations on them.

Matrix method of specifying the graph.

Basic operations on graphs.

Combining graphs.

Routes in graphs.

The concept of the route.

Routes in directed graphs.

Connectivity in graphs.

Connectedness and adjacency matrix of the graph.

Matrix vzaimodostizhimosti.

Trees.

Free trees.

Oriented, ordered and binary trees.

Euler and Hamiltonian graphs.

The problem of the bridges of Koenigsberg.

An algorithm for constructing Euler Euler cycle in the graph.

Hamiltonian graphs.

Estimating the number of Euler and Hamiltonian graphs

The fundamental cycles and cuts.

Fundamental cycles.

Incisions.

Planarity and coloring of graphs.

Planar graphs.

The coloring of graphs.

Algorithms coloring.

Communication theory of graphs with binary relations and vector spaces.

Relationship on the sets and graphs.

Vector spaces associated with graphs.

The shortest route in the graph.

Distances in graphs.

Bellman-Ford algorithm.

Coatings and independence.

Covers a multitude of vertices and edges.

Independent set of vertices and edges.

Dominating set.

The traveling salesman problem.

Statement of the Problem

Detours of vertices of depth and width.

The decision of the traveling salesman problem.

Flows in networks.

Basic definitions.

The theorem of Ford and Fulkerson.

An algorithm for constructing the maximum flow.

Network planning and management.

Elements of the network schedule.

Time parameters of the network schedule.

The distribution of limited resources.

An analysis of technical systems (for example, an electrical circuit).

Kirchhoff's law.

Basic equations.

Signal graphs.

General understanding of the signaling columns.

Conversion of signal graphs.