Math 581: Topics in Graph Theory
Fall 2006
Algebraic Graph Theory


The course is for students in the second year and higher; it is not an introductory graduate course. The absolute minimum requirement is a good understanding of abstraction and a solid modern algebra background (as from a graduate course), and the more graduate math you know, the better (that's the famous "mathematical maturity"). Previous knowledge of graph theory is not essential! If you aren't sure whether you might be interested or ready for this class, please see me.

We will use as textbook Algebraic Graph Theory by Chris Godsil and Gordon Royle (published by Springer Verlag), selected chapters, supplemented by my own (vastly improved??) interpretations using signed graphs. The main topics of the course are something like the following list (the details will be decided during the course, but I hope to cover Chapters 8-12 at least):

I will expect you, the students, to study the material and to work on as many of the exercises as you can. I will meet separately with each student frequently (every week or two) to discuss your progress and any questions you or I may have. I will frequently collect written work: see the homework assignments below. I will accept a second version of any problem, if you want to rewrite it for a better grade (or any other reason), but only within a reasonable time (let's say, about two weeks from when I returned the first version).

We meet MWF 1:10 - 2:10 in LN-2205. There will be student presentations, possibly during extra meetings.

Homework Assignments

You should do as many as you can of the exercises in the chapters we cover. Do a good job: it's better to do fewer well than more badly. I won't give specific assignments, except for a few problems to be handed in.


Hand-in Exercises

Problem "c.n" means Chapter c, #n. Your written work should be a final draft and logically complete (all necessary steps written and explained).

  1. Wed. 10/11 (due in class or before): 1.8, 1.10, 2.12, 3.2, 4.1, 4.A1.
  2. Mon. 11/6: 8.9 (with multiplicities), 8.A3.
  3. Wed. 11/8: 8.A6, 8.A9.
  4. Mon. 11/20: 8.A21, 10.2.
  5. Tues. 11/21 (or Wed. a.m.): 10.1, 10.A1, 10.A2.
  6. Fri. 12/8: 11.1, 11.A2.
  7. Fri. 12/8: 11.A3, 11.A5, 11.A8.
  8. Mon. 12/11 (may be postponed to Wed.): 11.A7.
  9. Wed. 12/13: (OMIT 12.A2), 12.A5, 12.5.

Additional Exercises

See the separate page.

Schedule of Presentations

The presentations will be on Tuesdays, 1:15 - 2:40 (but not usually using all that time) in LN-1402. The schedule:

To my home page.