Constructions of cospectral graphs with different zero forcing numbers

Several researchers have recently explored various graph parameters that can or cannot be characterized by the spectrum of a matrix associated with graph. In this paper, we show several NP-hard zero forcing numbers are not spectra types matrices particular, consider standard forcing, positive semidefinite and skew provide constructions infinite families pairs cospectral graphs, which different values for these numbers. We explore methods obtaining graphs including using products, joins, switching. Among these, construction involving regular adjacency graphs; regularity also implies cospectrality respect to other Laplacian, signless normalized Laplacian. where an arbitrarily large difference between their