Graph Theory

MATH 310 : Spring 2021

Department of Mathematics - SUNY Geneseo

Course Description

The purpose of this course is to introduce students to the fundamentals of graph theory and its applications. Topics covered include graphs, graph isomorphisms, trees, graph matrices and eigenvalues, strongly regular graphs, graph colorings, chromatic polynomials, planar graphs and the Four Color theorem. Students will use software to store, visualize, and manipulate graph models, and as a tool to explore basic properties of graphs.

Instructor

Cesar Aguilar, South Hall 325A

Office Hours

Tue 8:30-9:30, 10:45-11:45
Thu 10:45-11:45

Class Meetings

MWF 1:30-2:20, Bailey Hall 101
Zoom link

Software

Final Exam

Monday, May 17, 12:00-2:30pm

Textbook and Resources

Student File Upload

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Latest

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Homework

Title Due Date Week No.
Homework 1 - Graphs Feb 12, 2021 1
Homework 2 - Graph Isomorphisms Feb 28, 2021 3
Homework 3 - Special Graphs Mar 8, 2021 5
Homework 4a - Adjacency Matrix Mar 23, 2021 7
Homework 4b - Roots of Polynomials Mar 25, 2021 8
Homework 5 - Graph Eigenvalues Apr 2, 2021 9
Homework 6 - Cospectral Graphs Apr 8, 2021 10
Homework 7 - Laplacian Matrices Apr 21, 2021 11

Schedule

Week 1  Feb 01 - Feb 05
Introduction, Graphs, Python
Topics: Introduction, Graphs, Python
What to Read: 1.1
Feb 01 First day of classes
HOMEWORK HW 1DUE: Feb 12
Week 2  Feb 08 - Feb 12
Rudiments of graph theory
Topics: Rudiments of graph theory
What to Read: 1.2
Files:
  1. gdraw.py - A simple class to draw graphs in Python
  2. examples.py - Examples on how to use gdraw
HW DUE HW 1DUE: Feb 12
Week 3  Feb 15 - Feb 19
Permutations, Isomorphisms
Topics: Permutations, Isomorphisms
What to Read: 1.3-1.4
HOMEWORK HW 2DUE: Feb 28
Week 4  Feb 22 - Feb 26
Special Graphs, Operations on Graphs
Topics: Special Graphs, Operations on Graphs
What to Read: 1.5
Week 5  Mar 01 - Mar 05
Trees
Topics: Trees
What to Read: 1.6
Mar 02 Rejuvenation Day - No classes
HW DUE HW 2DUE: Feb 28
HOMEWORK HW 3DUE: Mar 08
NEXT WEEK Test 1 on Mar 12, 1:30 PM – 2:20 PM
Week 6  Mar 08 - Mar 12
Catch-up and Review for Test 1
Topics: Catch-up and Review for Test 1
HW DUE HW 3DUE: Mar 08
TEST 1 Mar 12, 1:30 PM – 2:20 PM
Week 7  Mar 15 - Mar 19
Adjacency Matrix
Topics: Adjacency Matrix
What to Read: 2.1
HOMEWORK HW 4ADUE: Mar 23
Week 8  Mar 22 - Mar 26
Roots of a Polynomial
Topics: Roots of a Polynomial
What to Read: 2.2
Mar 24 Rejuvenation Day - No classes
HW DUE HW 4ADUE: Mar 23
HOMEWORK HW 4BDUE: Mar 25
HW DUE HW 4BDUE: Mar 25
Week 9  Mar 29 - Apr 02
Graph Eigenvalues
Topics: Graph Eigenvalues
What to Read: 2.3
HOMEWORK HW 5DUE: Apr 02
HW DUE HW 5DUE: Apr 02
Week 10  Apr 05 - Apr 09
Cospectral Graphs
Topics: Cospectral Graphs
What to Read: 2.4
HOMEWORK HW 6DUE: Apr 08
HW DUE HW 6DUE: Apr 08
NEXT WEEK Test 2 on Apr 12, 1:30 PM – 2:30 PM
Week 11  Apr 12 - Apr 16
Laplacian Matrices
Topics: Laplacian Matrices
What to Read: 4.1
HOMEWORK HW 7DUE: Apr 21
TEST 2 Apr 12, 1:30 PM – 2:30 PM
Week 12  Apr 19 - Apr 23
The Matrix Tree Theorem, Applications
Topics: The Matrix Tree Theorem, Applications
What to Read: 4.2
Apr 22 Rejuvenation Day - No classes
HW DUE HW 7DUE: Apr 21
Week 13  Apr 26 - Apr 30
PageRank
Week 14  May 03 - May 07
PageRank
Week 15  May 10 - May 14
Presentations
Topics: Presentations
May 12 Last day of classes
NEXT WEEK Final Exam on May 17, 12:00 PM – 2:30 PM
Week 16  May 17 - May 21
Final Exam
Topics: Final Exam
FINAL EXAM May 17, 12:00 PM – 2:30 PM

Syllabus

Learning Outcomes

Upon successful completion of MATH 310 - Graph Theory, a student will be able to:

    Grading Scheme

    Below is the tentative course grading scheme. The grading scheme may change during the semester at the discretion of the instructor. Any changes to the grading scheme will be announced in class before the final exam. If homework assignments are done in groups, then a student must achieve a passing grade in all individual assessments (e.g., tests and final exam) to pass the course.

    ItemPercentage
    Homework30
    Tests30
    Presentation5
    Report5
    Final Exam30
    GradePercentage
    A94-100
    A−90-93
    B+87-89
    B83-86
    B−80-82
    C+77-79
    C73-76
    C−70-72
    D60-69
    E< 60

    Tests and Exam

    There will be 3-4 tests scheduled evenly throughout the semester. The final exam is scheduled for Monday, May 17, 12:00-2:30pm. The final exam will be cumulative, that is, any topic covered in the course could be tested in the final exam. There will be no make-up for a missed test or final exam under any circumstances. If a student misses a test and can present evidence of an extenuating circumstance then the weight of the missed test will be redistributed to the final exam weight. Having the cold or flu is not an extenuating circumstance. Examples of extenuating circumstances include a medical emergency, a serious prolonged illness, or the death of a member of your immediate family.

    Homework

    There will be approximately one homework assignment per week. Students will be given approximately one week to complete a homework assignment. All homework assignments must be written in LaTeX (not Word). Instructions will be given on the first day of class on how to obtain and use the LaTeX program. The quickest way to get started with LaTeX is to use the online application called Overleaf and by reading the Learn LaTeX in 30 Minutes tutorial. If homework assignments are done in groups, then a student must achieve a passing grade in all individual assessments (e.g., tests and final exam) to pass the course. I encourage you to collaborate with your colleagues on your assignments/labs but your final submitted work should be your own (see Academic Dishonesty statement below).

    Final Project

    Students will be divided into groups of two and each group will present a topic closely related to the course but on material not directly covered in the course. Topics will be chosen from several undergraduate level journal papers that will be provided by the instructor or the topic can be chosen by the student. Each group will write a summary of their topic in the form of a report. The presentations will be held during the last week of class and the report is due on the last day of class.

    Technology

    Calculators are not permitted during the tests or final exam. However, I encourage you to use your calculator, Maple and other math software, WolframAlpha, and other forms of technology as you study and do your assignments. Both Maple and Mathematica can be downloaded from SUNY Geneseo Software page.

    Office Hours and Math Learning Center

    I encourage you to come to my office (South Hall 325A) whenever you are having trouble with any part of the course material, seeking academic advice, or you just want to chat about mathematics in general. If you want to meet with me outside of my office hours, you will need to make an appointment, preferably via email. I also encourage you to visit the Math Learning Center located in South Hall 332 where you can receive free tutoring on a walk-in basis by highly qualified upper level students. Access to in-person office hours and to the MLC will depend on social distancing guidelines set by the College.

    Email Communication

    I will do my best to reply to student email regarding the logistics of the course within 24 hours during the working week (Mon-Fri). However, due to the potential large volume of emails, inquiries regarding homework problems and/or specific course content should be made during office hours or after class.

    Academic Dishonesty and Plagiarism

    Please read, and follow, Geneseo's Academic Dishonesty and Plagiarism policy. Below is the definition of plagiarism and its consequences as described in SUNY Geneseo's Academic Dishonesty and Plagiarism statement:

    Plagiarism is the representation of someone else's words or ideas as one's own, or the arrangement of someone else's material(s) as one's own. Such misrepresentation may be sufficient grounds for a student's receiving a grade of E for the paper or presentation involved or may result in an E being assigned as the final grade for the course.

    If there is sufficient evidence of academic dishonesty on a homework assignment, all students involved will receive a zero score on the homework assignment and I will provide the department chairperson, the dean of academic planning and advising, and the student(s) with a written report of the violation, the penalty imposed and the counseling provided to the students involved. A second instance of academic dishonesty on a homework assignment will result in a final grade of E for the course for all students involved. Academic dishonesty on a test/final exam will result in a final grade of E for the course.

    Academic Accommodations

    SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility (OAS) will coordinate reasonable accommodations for persons with disabilities to ensure equal access to academic programs, activities, and services at Geneseo.

    Students with approved accommodations may submit a semester request to renew their academic accommodations. Please visit the OAS website for information on the process for requesting academic accommodations.

    Questions? Contact the OAS by email, phone, or in-person:

    Office of Accessibility Services
    Erwin Hall 22
    585-245-5112
    access@geneseo.edu