Department of Mathematics

Combinatorics and Graph Theory

  •  Robert Davis, Colgate University
  •  Analyzing Power Grid Stability via the Dragon Marriage Theorem,, passcode: MthMus
  •  10/14/2020
  •  3:00 PM - 3:50 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Bruce E Sagan (

One real-life situation application of graph theory is the study of electrical grids: they have to be constructed carefully since unstable grids can lead to brownouts, blackouts, damaged equipment, or other possible problems. If we know the connections in the grid that we want, how can the voltages at each node be coordinated in a way that makes sure the network stays stable? This is a difficult question, but even knowing the number of ways to keep a network stable can help. In this talk, we will see how to count the number of "stable solutions" using geometric and algebraic methods. These methods will help us obtain recurrences for networks satisfying mild conditions. Consequently, we obtain explicit, non-recursive formulas for the number of stable solutions for a large class of outerplanar graphs, and conjecture that the formula holds for all outerplanar graphs. One of the keys to our results: studying dragons and the havoc they wreak on fictional medieval villages.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science