Information Of Programmes

INSTITUTE OF SCIENCE / MAT606 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT606

Course Title: SPECTRAL GRAPH THEORY II

Theoretical+Practice: 3+0

ECTS: 6

Year/Semester of Study

1 / Spring Semester

Level of Course

3rd Cycle Degree Programme

Type of Course

Optional

Department

MATHEMATICS (DOCTORATE DEGREE)

Pre-requisities and Co-requisites

None

Mode of Delivery

Face to Face

Teaching Period

14 Weeks

Name of Lecturer

SEZER SORGUN (ssorgun@nevsehir.edu.tr)

Name of Lecturer(s)

Language of Instruction

Turkish

Work Placement(s)

None

Objectives of the Course

To understand the spectral characterizations of graph matrices.

Learning Outcomes		PO	MME
The students who succeeded in this course:
LO-1	Can apply the spectral techniques.	PO-3 Students will be dominated by current issues in mathematics.	Examination
LO-2	Can have the knowledge about spectrums of Laplacian matrix of graph	PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.	Performance Project
LO-3	Can have the ability of spectral characterization for matrices represented by graph	PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.	Examination Term Paper
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
Star complements, Graphs with least eigenvalue -2 and its spectral properties, Spectral techniques on some special graphs, The Matrix-Tree teorem, The largest Laplacian eigenvalue, Algebraic connectivity, The normalized Laplacian matrix, The signless Laplacian, Integral graphs, Applications of spectral graph theory on some fundamental sciences such as physics, chemistry, etc.
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Star complements	Teaching topic and applications
2	Graphs with least eigenvalue -2	Teaching topic and applications
3	Spectral technique	Teaching topic and applications
4	Decompositions of complete graphs	Teaching topic and applications
5	The Friendship teoremi	Teaching topic and applications
6	Laplacian spectrum	Teaching topic and applications
7	The matrix-tree teorem	Teaching topic and applications
8	mid-term exam
9	The largest Laplacian eigenvalue	Teaching topic and applications
10	Algebraic Connectivity	Teaching topic and applications
11	Laplacian eigenvalues and graph structures	Teaching topic and applications
12	The Signless Laplacian	Teaching topic and applications
13	Eigenvectors and structure	Teaching topic and applications
14	Reconstructing the characteristic polynomial, integral graphs	Teaching topic and applications
15	Applications of spectral graph theory on fundamental science	Teaching topic and applications
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	An introduction to the theory of Graph Spectra, D.Cvetkovic,P.Rowlinson and S.Simic, London Mathematical Society Student Text 75, Cambridge Uni.Press,2010.
2	Algebraic graph theory, U. Knauer, Studies in Math. 41, Berlin,2011
Required Course instruments and materials

Assessment Methods
Type of Assessment	Week	Hours	Weight(%)
mid-term exam	8	2	30
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project	7	2	10
8.Term Paper	14	2	10
9.Project
final exam	16	2	50

Student Work Load
Type of Work	Weekly Hours	Number of Weeks	Work Load
Weekly Course Hours (Theoretical+Practice)	3	14	42
Outside Class
a) Reading	2	14	28
b) Search in internet/Library	2	14	28
c) Performance Project	3	7	21
d) Prepare a workshop/Presentation/Report			0
e) Term paper/Project	3	7	21
Oral Examination			0
Quiz			0
Laboratory exam			0
Own study for mid-term exam	3	8	24
mid-term exam	2	1	2
Own study for final exam	3	8	24
final exam	2	1	2
			0
			0
Total work load;			192