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Monographic lecture II


Some basic information about the module

Cycle of education:
2018/2019
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Mathematics
The area of study:
sciences
The profile of studing:
The level of study:
first degree study
Type of study:
full time
discipline specialities :
Applications of Mathematics in Computer Science, Applications of Mathematics in Economics
The degree after graduating from university:
The name of the module department :
Departament of Discrete Mathematics
The code of the module:
1073
The module status:
mandatory for teaching programme with the posibility of choice Applications of Mathematics in Economics
The position in the studies teaching programme:
sem: 5 / W30 C15 / 3 ECTS / Z
The language of the lecture:
Polish
The name of the coordinator:
Paweł Bednarz, PhD

The aim of studying and bibliography

The main aim of study:
Familiarising students with chosen issues concering the theory of digraphs and networks

The general information about the module:
Subject of classes was chosen by students.

Bibliography required to complete the module
Bibliography used during lectures
1 R.J. Wilson Wprowadzenie do teorii grafów PWN, Warszawa. 2000
2 R. Diestel Graph Theory Springer GTM 173, 5th edition. 2016
3 A. Włoch, I. Włoch Matematyka dyskretna. Podstawowe metody i algorytmy teorii grafów Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów . 2017
Bibliography used during classes/laboratories/others
1 R.J. Wilson Wprowadzenie do teorii grafów PWN, Warszawa. 2000
2 R. Diestel Graph Theory Springer GTM 173, 5th edition. 2016
3 A. Włoch, I. Włoch Matematyka dyskretna. Podstawowe metody i algorytmy teorii grafów Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów . 2017
Bibliography to self-study
1 J. Bang-Jensen, G.Z. Gutin Digraphs: theory, algorithms and applications Springer Science & Business Media. 2008

Basic requirements in category knowledge/skills/social competences

Formal requirements:
Requirements accordant with Rules and Regulations of studies

Basic requirements in category knowledge:
Student has knowledge in the fields of discrete mathematics.

Basic requirements in category skills:
Student knows, understands and can apply concepts of discrete mathematics.

Basic requirements in category social competences:
Student has the ability to independent and collaborative lerning, is aware of the level of his knowledge and understands the need of self-learning.

Module outcomes

MEK The student who completed the module Types of classes / teaching methods leading to achieving a given outcome of teaching Methods of verifying every mentioned outcome of teaching Relationships with KEK Relationships with OEK
MEK01 The student knows basic definitions and theorems of digraph theory lecture, classes test K-W01+
K-W02++
K-W03+
K-W04+
K-W05+
K-W06+
K-U01+
 W1+
W2+
W3+
U6+
MEK02 The student knows selected algorithms in digraphs related to optimization problems lecture, classes test K-W02+
K-W03+
K-W04+
K-W05+
K-W06+
K-U01+
 W2+
W3+
U6+
MEK03 The student can use methods of digraph theory for solving discrete problems lecture, classes test K-W01+
K-W04+
K-W05+
 W1+
W3+

The syllabus of the module

Sem. TK The content realized in MEK
5 TK01 Basic concepts of graph theory. Introduction to digraph theory. Connectivity and strong connectivity of digraphs, directed trees, tournaments, Euler and Hamilton cycles in digraphs. W01-W10, C01-C05 MEK01 MEK02 MEK03
5 TK02 weighted digraphs. Algorithms for finding distances in digraphs. Breadth-first search, Dijkstra's algorithm, the Bellman-Ford-Moore algorithm. Diameter, radius and kings in digraphs. The travelling salesman problem and the Chinese postman problem. W11-W20, C06-C10 MEK01 MEK02 MEK03
5 TK03 Networks and flows. The residual network. The maximum flow problem. The Ford-Fulkerson algorithm. Minimum cost flows. The Busacker-Gowen algorithm. Application of flows. The Chinese postman problem and maximum matchings in bipartite graphs. W21-W30, C11-C13 MEK01 MEK02 MEK03

The student's effort

The type of classes The work before classes The participation in classes The work after classes
Lecture (sem. 5) contact hours: 30.00 hours/sem.
 complementing/reading through notes: 6.00 hours/sem.
Class (sem. 5) The preparation for a Class: 15.00 hours/sem.
 contact hours: 15.00 hours/sem.
Advice (sem. 5) The preparation for Advice: 6.00 hours/sem.
 The participation in Advice: 3.00 hours/sem.
Credit (sem. 5)

The way of giving the component module grades and the final grade

The type of classes The way of giving the final grade
Lecture A credit for the lecture is based on attendance at the lectures.
Class Student has to get at least 50% points on the test during classes.
The final grade

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile yes

1 P. Bednarz; A. Michalski The (1,2)-intersection index of a graph with large minimum degree and its application in crisis management 2024
2 P. Bednarz; A. Szynal-Liana Bihyperbolic Numbers of the Fibonacci Type and Triangular Matrices (Tables) 2024
3 P. Bednarz; M. Pirga On Proper 2-Dominating Sets in Graphs 2024
4 P. Bednarz Relations between the existence of a (2 − d)-kernel and parameters γ2(G), α(G) 2022
5 P. Bednarz On (2-d)-Kernels in the Tensor Product of Graphs 2021
6 P. Bednarz; A. Michalski On Independent Secondary Dominating Sets in Generalized Graph Products 2021
7 P. Bednarz; N. Paja On (2-d)-Kernels in Two Generalizations of the Petersen Graph 2021