Fall 2021 - MATH 820 G100
Graph Theory (4)
Class Number: 2563
Delivery Method: In Person
Overview
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Course Times + Location:
Sep 8 – Dec 7, 2021: Wed, Fri, 2:30–4:20 p.m.
Burnaby
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Instructor:
Matthew DeVos
mdevos@sfu.ca
Description
CALENDAR DESCRIPTION:
Algebraic graph theory, extremal graph theory, coloring problems, path and cycle structure of graphs, application of graphs, hypergraphs, and current research topics.
COURSE DETAILS:
This course is an introduction to modern algebraic graph theory, concerning both graphs with special algebraic properties and the use of algebraic techniques to study arbitrary graphs. The first portion of the course is devoted to vertex transitive graphs: We will study their properties and their interconnection to additive combinatorics. The second part of the course will introduce spectral methods and these will be used to investigate both strongly regular graphs and arbitrary graphs. Students will be expected to do a project that will involve understanding a significant research paper (or equivalent) and then present this material to the class (these presentations will form the final part of the course).
Part 1: Vertex Transitive Graphs
- Connectivity
- Growth
- Tutte’s bound on arc-transitivity
- Cayley graphs, groups, and additive combinatorics
- Kneser Graphs (and colouring)
Part 2: Spectral Methods
- Matrix Theory
- Strongly Regular Graphs
- Line Graphs
- Laplacians and planarity
Grading
- Homework 40%
- Exam (late in term) 20%
- Project 40%
NOTES:
Prerequisite: MATH 445 or equivalent
Materials
REQUIRED READING:
Godsil, C. D. & Royle, G. (2001). Algebraic graph theory /. Springer-Verlag.
ISBN: 9780387952208
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the University community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html
TEACHING AT SFU IN FALL 2021
Teaching at SFU in fall 2021 will involve primarily in-person instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place. Whether your course will be in-person or through remote methods will be clearly identified in the schedule of classes. You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).
Enrolling in a course acknowledges that you are able to attend in whatever format is required. You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.
Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the fall 2021 term.