Zero-nonzero tree patterns that allow

Abstract

For , let . A zero-nonzero pattern of order n allows if , the inertia set of , and requires if . The study of zero-nonzero patterns allowing was introduced by Berliner et al. [Inertia sets allowed by matrix patterns. Electron J Linear Algebra. 2018;34:343–355]. In this paper, we give characterizations of irreducible zero-nonzero path patterns and double-star patterns that allow . Moreover, all irreducible zero-nonzero tree patterns of order 5 and 6 that allow are also characterized.