27th Conference of the International Linear Algebra Society (ILAS 2026)

Tools for Determining the Minimum Rank of a Graph

May 21, 2026, 2:25 PM

25m

Goodwin Hall 244

Minisymposium Talk The Inverse Eigenvalue Problem of a Graph and Zero Forcing The Inverse Eigenvalue Problem of a Graph and Zero Forcing

Speaker

Mark Hunnell (Winston-Salem State University)

Description

The minimum rank of a graph $G$ of order $n$ is the smallest possible rank over all real symmetric $n\times n$ matrices $A$ whose $(i,j)$th entry, for $i\neq j$, is nonzero whenever $ij$ is an edge of $G$ and zero otherwise. We discuss some refinements of techniques currently in the literature to determine the minimum rank of a graph, some new tools to bound this value, and an approach for understanding the gaps in values between parameters used to bound the minimum rank of a graph. We also discuss implementations of known techniques, algorithmic improvements, and applications in computer assisted experimentation for the minimum rank problem.