Speaker: Leslie Hogben
Affiliation: Department of Mathematics, Iowa State University
Title: Power domination and zero forcing: Using graphs to model real-world problems
Abstract:
A graph is a set of vertices and set of edges of two element sets of vertices. A graph can be used to model connections between vertices, such as airline routes between cities, internet connections, a quantum system, or an electric power network.
Power domination and zero forcing are related coloring processes on graphs. We start with a set of vertices colored blue and the rest colored white. We apply a color change rule to color the white vertices blue. A set of blue vertices that can color all vertices blue by using the power domination color change rule (or zero forcing color change rule) is called a power dominating set (or a zero forcing set). Finding a such set allows us to solve various problems, and a minimum such set can provide an optimal solution.
In an electric power network, a power dominating set (blue vertices) gives a set of locations from which monitoring units can observe the entire network. In a quantum system, a zero forcing set (blue vertices) gives a set of locations from which the entire system can be controlled.
This talk will describe power domination and zero forcing processes on graphs and some of their applications.
Date: April 27, 2017
Time: 11am -12.00 noon
Place: UAC 474
Speaker’s bio: Leslie Hogben received her Ph. D. from Yale in mathematics under Nathan Jacobson in nonassociative ring theory and now does research in the area of linear algebra, specializing in combinatorial matrix theory.
Prof. Hogben is the co-director of the Iowa State University Mathematics Department’s NSF sponsored Research Experiences for Undergraduates program. She is also a co-organizer of Research Experiences for Undergraduate Faculty (REUF), a program supported by the American Institute of Mathematics (AIM), the Institute for Computational and Experimental Mathematics (ICERM), and the National Science Foundation (NSF).
Prof. Hogben is the Associate Director for Diversity at the American Institute of Mathematics, San Jose, CA. She is also the author of the book “Handbook of Linear Algebra” (CRC Press, 1st.ed. 2007 and 2nd.ed. 2014) and a co-editor of the book “Recent Trends in Combinatorics” (Springer, 2016).