Iğdır University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT-23-210	GRAF TEORİ II	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

To learn the basic concepts of graphs and matrices.

Name of Lecturer(s)

Dr. Öğr. Üyesi Ezgi KAYA

Learning Outcomes

1	Writes Adjacency matrix and Laplacian matrix.
2	Finds spectral radius and Laplacian spectral radius.
3	Researchs some special graphs and their some special matrices.
4	Binds abstract concepts in mathematics to specific events using scientific methods; analyzes and interprets the results.

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

It is need to know the basic facts of mathematics courses in the graduate level.

Recommended Optional Programme Components

Course Contents

Basic Concepts of Matrix, Fundamental Concepts of Graphs, Adjacency Matrix and its Eigenvalues of a Graph Incidence Matrix and Degree Matrix, Finding a Boundary for the Spectral Radius of a Graph, Randic Matrix of a Graph and Eigenvalues, Laplacian Matrix and its Eigenvalues of a Graph, Normalized Laplacian Matrix and Signless Laplacian Matrix, Signless Laplacian Matrix and its Eigenvalues, Rings, Paths and Cayley Graphs Distance Matrix and its Eigenvalues of a Graph, Matrices and Eigenvalues of Digraphs, Matrices and Eigenvalues of Weighted Graphs

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Basic Concepts of Matrix
2	Fundamental Concepts of Graphs
3	Adjacency Matrix and its Eigenvalues of a Graph
4	Incidence Matrix and Degree Matrix
5	Finding a Boundary for the Spectral Radius of a Graph
6	Randic Matrix of a Graph and Eigenvalues
7	MIDTERM EXAM
8	Laplacian Matrix and its Eigenvalues of a Graph
9	Bir Grafın Normalleştirilmiş Laplacian Matrisi ve Özdeğerleri
10	Signless Laplacian Matrix and its Eigenvalues
11	Cycles, Paths and Cayley Graphs
12	Distance Matrix and its Eigenvalues of a Graph
13	Matrices and Eigenvalues of Digraphs
14	Matrices and Eigenvalues of Weighted Graphs
15	Problem Solving

Recommended or Required Reading

Harju T., Lecture Notes in Graph Theory, Department of Mathematics, University of Turku, 2002. Jonathan Gross, Jay Yellen, Graph thery and and its applications CRC pres,1998. Chartrand, G., Lesniak, L., Graphs and digraphs Chapman & Hall.,.1996.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	1	1
Final Examination	1	2	2
Attending Lectures	14	3	42
Question-Answer	14	3	42
Brain Storming	14	3	42
Criticising Paper	5	2	10
Self Study	14	3	42
TOTAL WORKLOAD (hours)			181

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11
LO1	4	4	4	4	4	4	4	4	4	4	4
LO2	4	4	4	4	4	4	4	4	4	4	4
LO3	4	4	4	4	4	4	4	4	4	4	4
LO4	4	4	4	4	4	4	4	4	4	4	4

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High