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Recurrence equations. Graph types and families, power and complement of a graph, weighted graphs, products of two graphs. Isomorphism of graphs. Algebraic representations of the graph: adjacency matrix, incidence matrix, lists of adjacencies.
Calculating a number of paths using adjacency matrix. Conditions for the existence of Euler and Hamilton cycles. Definitions and basic properties. Binary tree.
Tree encoding method simple and reverse Prufer code. Cayley theorem about number of labeled trees in the complete graph. Finding a number of spanning trees using Laplace matrix of a graph. Independent sets of vertices. Fibonacci number of a graph. Determination of maximal independent sets of vertices using Boolean algebra.
Independence of edges - matchings. Finding maximum matching in the bipartite graph by augmenting path algorithm.
Vertex coloring. Chromatic number and chromatic polynomial. Edge coloring - chromatic index. Dmytryszyn, G. Kenneth A. Ross, Charles R. Deo, J. Ronald L. Graham, Donald E. Student knows the basic combinatorial objects and can consider them in three aspects: the existence, number and systematic generation.
Student can build a model of the problem and solve it. Student can use the Maxima CAS to perform calculations, generating combinatorial objects and to study the properties - at a basic level. Skip to main menu Skip to submenu Skip to content. Print syllabus. Choosen plan division: this week course term. Course descriptions are protected by copyright. Reset Password You are not logged in log in.
Department of Electrical and Computer Fundamentals. I-go stopnia. The syllabus - Mathematical induction. Planar graphs. Graphs on surfaces. Bibliography used during lectures R. The student who completed the module. The ways of veryfing every mentioned outcome of teaching. Student knows the basic concepts, theorems and algorithms of the graph theory. Assessment methods and assessment criteria:. Choosen plan division: this week course term see course schedule. Laboratory, 15 hours more information Lecture, 30 hours more information.
Class, 15 hours more information Laboratory, 15 hours more information Lecture, 30 hours more information.
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The name of the module: Discrete mathematics 1. The name of the faculty organization unit: The faculty Electrical and Computer Engineering. The name of the module department : Department of Electrical and Computer Fundamentals. The contact details of the coordinator: the building B, room , phone 17 , aszczep prz. The main aim of study: The aim of this educational module is to familiarize students with the basic mathematical methods used for analyzing and solving computer math problems. The material implemented in this course can be divided into two main parts: combinatorics and graph theory. Students will learn selected combinatorial objects generation algorithms and graph theory ilustrated by algorithms.
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Embed Size px x x x x Aardal, G. Nemhauser, and R. Discrete Optimization. Abramow, M. Mariniczew, and P. Metody analizysieciowej w planowaniu i zarzadzaniu.