Computational Structures II

Chip Klostermeyer

wkloster@unf.edu

Goals: Students will improve their mathematical and problem-solving ability, be able to present and discuss mathematical concepts, be able to find information in the scholarly literature, be able to read and synthesize mathematical papers into a survey paper format, and be able to write a program with a graphical user interace that manipulates graphs.

Evaluation:

  • Attendance (10%, 1% deduction for each class missed))
  • Problem presentation (10%, must present and discuss in class an open problem from one of the web sites below)
  • Term paper (25%, 7-10 pages, must survey a problem from one of the topics below).
  • Program (25%)
  • Homework (5%)
  • Final Exam (25%)

    Open Problems Links:

    Open 1

    Open 2

    Open 3 (Excellent, long List!)

    Open 4 (Wiki)

    Open 5

    Term Paper Topics (must get approval if choosing a topic not on this list)

  • Domination (gamma, specifically)
  • Roman Domination
  • Connected Dominating Sets (should include discussion of application in wireless networks)
  • Total domination
  • Irredundance and the domination chain
  • Independent Domination (may include perfect domination and efficient domination)
  • Global Alliances/Global Secure sets
  • Paired Domination
  • Facility Location Problems
  • Broadcast Functions in Graphs
  • Chessboard Domination
  • Power Domination in Graphs
  • Cops and Robbers
  • Coloing games (e.g. game chromatic number)

    Your paper should explain the problem, give examples, disucss the main results in the area, and disucss the important open problems and conjectures. Your paper should survey material from at least two (preferably more) papers from the mathematical literature. Please see the UNF library for many journals that are in electronic form: UNF Library . Some of the appropriate journals accessible there include Discrete Mathematics, Discrete Applied Mathematics, Journal of Graph Theory, Graphs and Combinatorics. Many papers (that were published in refereed journals) can also be found on the author's web site or from Google Scholar .

    It is suggested that you submit a rough draft to the instructor prior to the due date.

    Program and term paper due the last scheduled day of class.