DisCoMath Seminar: A Nordhaus-Gaddum conjecture on the eigenvalues of graphs and their structures
Discrete & Computational Math Seminar (DisCoMath)
A Nordhaus-Gaddum conjecture on the eigenvalues of graphs and their structures
Dr. Shahla Nasserasr
Assistant Professor
School of Mathematical Sciences, RIT
Abstract:
For a graph G on n vertices, and a parameter p related to G, a Nordhaus-Gaddum type problem is to find an upper bound and a lower bound as functions of n for p(G)+p(G¯¯¯¯). When p(G)=q(G), the minimum number of distinct eigenvalues of G (introduced in the previous talk by Dr. Rooney), it is conjectured that the upper bound is n+2. The conjecture is proved for many families of graphs. In this talk, we will focus on this conjecture and the families of graphs for which the conjecture is true. The talk will be out of the paper https://www.sciencedirect.com/science/article/pii/S0024379518305561
Speaker Bio:
Dr. Nasserasr is an Assistant Professor in the School of Mathematical Sciences at RIT. She received her Ph.D. in matrix analysis from the College of William and Mary in 2010. Prior to joining RIT in 2020, she was an Associate Professor of Mathematics at Brandon University, Canada. Dr. Nasserasr’s research interests include combinatorial matrix theory, inverse eigenvalue problem, totally positive matrices, and graph theory.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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Open to the Public
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