Topics in Combinatorics

Revised Report 2 is due by 12:00 noon, Thursday, April 30. 


MAD 7397 – 0017

Spring 2020



Time:      MWF period 5 

Place:     Little 207

Phone:    352-294-2339

Office:     438 Little Hall



References (not required):

           Graph Theory by R. Diestel

           Introduction to Graph Theory by D. West

           Algebraic Graph Theory by Godsil and Royle



Office Hours:                    Monday, Wednesday, Friday     period 6

                                             (or by appointment)






Topics in Graph Theory – Geometric, Algebraic, Topological

The selected topics illustrate the interplay between graph theory and other branches of mathematics.

    • Art Gallery Problem
    • Page Rank
    • Geometric Representations of Graphs
    • …….Straight-line embedding
    • …….Thrackles
    • …….Steinitz Theorem
    • …….Rubber band representation
    • …….Representation as a tiling by squares
    • …….Coin representation – Koebe’s Theorem, Lipton-Tarjan separator theorem
    • …….Orthogonal representation – Shannon capacity
    • Spectral Graph Theory
    • …….Laplacian of a graph
    • …….Isoperimetric Problems
    • …….Expanders
    • Graph Automorphisms and Homomorphisms
    • Knots and Graphs

Because classes are now online, and assuming that this is the case for the remainder of the semester, the assignment is as follows.   You may:

  1.  Pick a subject of your own choosing, related to graph theory, that is new to you, and investigate that subject.
  2.  Pick a subject or subjects from the text Algebraic Graph Theory by Godsil and Royle (can be download free from, and read about and investigate that subject.
  3. Read and investigate subjects that I suggest from Algebraic Graph Theory by Godsil and Royle.  

In all three cases, submit to me via email in pdf format, a short summary, in your own words, of what you have learned, providing the essentials of the subject.  There are approximately 6 weeks left in the semester.  You are requested to submit two such reports, the first to reach me no later than April 3, the second by April 24.  Please let me know which of the three alternatives you choose by March 18.  


Course Evaluation:

The grade is based on classroom participation and attendance, and (because of the transition to online classes) the assignment in the section above.





Welcome to Topics in Combinatorics

Students with disabilities requesting accommodations should first register with the Disability Resource Center (352-392-8565) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.

The course will be conducted in accordance with the academic honesty policy, and policy regarding the use of copyrighted material.

“Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found at: attendance policies.

Information on current UF grading policies for assigning grade points may be found at: grades.

Students are expected to provide feedback on the quality of instruction in this course by completing a course evaluation online via GatorEvals. Guidance on how to give feedback is available at Students will be notified when the evaluation period opens and can complete evaluations through the email they receive from GatorEvals, in their Canvas course menu under GatorEvals, or via Summaries of course evaluations results are available to students at