The inverse eigenvalue problem for probe graphs

• DOI: 10.48550/arxiv.2402.18670
• Publication Date: 2024-02-28
• Authors: Emelie Curl; Jürgen Kritschgau; Carolyn Reinhart; Hein van der Holst

In this paper, we initiate the study of inverse eigenvalue problem for probe graphs. A graph is a whose vertices are partitioned into and non-probe such that form an independent set. general, used to represent set graphs can be obtained by adding edges between vertices. The considers family matrices zero-nonzero pattern defined asks which spectra achievable in family. We ask same question start establishing bounds on maximum nullity defining zero forcing number. Next, focus two parallel paths, unique (standard) number two. partially characterize prove some necessary structural results about Finally, minimum rank $0, 1, 2, n-2,$ $n-1$.