DisCoMath Seminar: Achievable Multiplicity Partitions of a Graph
Achievable Multiplicity Partitions of a Graph
Dr. Shahla Nasserasr
School of Mathematical Science, RIT
For a graph G, the class of real-valued symmetric matrices whose zero-nonzero pattern of off-diagonal entries is described by the adjacencies in G is denoted by S(G). The inverse eigenvalue problem for the multiplicities of the eigenvalues of G is to determine for which ordered list of positive integers m1≥m2≥⋯≥mk with ∑ki=1mi=|V(G)|, there exists a matrix in S(G) with distinct eigenvalues λ1,λ2,⋯,λk such that λi has multiplicity mi. A related parameter is q(G), the minimum number of distinct eigenvalues of a matrix in S(G). We study graphs that can achieve two distinct eigenvalues (q(G)=2) with given multiplicities. This is joint work with the Discrete Mathematics Research Group of Regina.
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.
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