Information Of Programmes

INSTITUTE OF SCIENCE / MAT605 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT605

Course Title: SPECTRAL GRAPH THEORY I

Theoretical+Practice: 3+0

ECTS: 6

Year/Semester of Study

1 / Fall 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 teach topics about spectral graph theory.

Learning Outcomes		PO	MME
The students who succeeded in this course:
LO-1	Can define various types of graph spectra.	PO-3 Students will be dominated by current issues in mathematics.	Examination
LO-2	Can have knowledge about graph matrices and apply the topics of linear algebra.	PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field.	Performance Project
LO-3	Can do spectral characterizations	PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.	Term Paper Practice Exam
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
Graph spectra, graph operations and modifications, Characterizations by spectra, Spectral characterizations of certain classes of graphs, The graph isomorphism problem
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Graph spectra	Teaching topic and applications
2	Some results from linear algebra	Teaching topic and applications
3	Graph operations and modifications	Teaching topic and applications
4	Line graphs and related operations	Teaching topic and applications
5	Spectra of graphs of particular types	Teaching topic and applications
6	Counting certain subgraphs	Teaching topic and applications
7	Connectedness and metric invariants	Teaching topic and applications
8	mid-term exam
9	Regularrity and bipartiteness	Teaching topic and applications
10	Spectral bounds for graph invariants	Teaching topic and applications
11	Constraints on special eigenvalues	Teaching topic and applications
12	Spectral characterizations of certain classes of graphs	Teaching topic and applications
13	Cospectral graphs and the graph isomorphism problem	Teaching topic and applications
14	Cospectral graphs and the graph isomorphism problem	Teaching topic and applications
15	Characterizations by eigenvalues and angles	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
The books of lecture

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