The spectra of digraphs with Morita equivalent C⁎-algebras

Eilers et al. have recently completed the geometric classification of unital graph $C^\ast$-algebras up to Morita equivalence using a set moves on corresponding digraphs. We explore question whether these preserve nonzero elements spectrum finite digraph, which in this paper is allowed loops and parallel edges. consider several different digraph spectra that been studied literature, answering for Laplace adjacency spectra, their skew counterparts, symmetric spectrum, line Hermitian normalized Laplacian, considering most cases two ways can be defined presence show are preserved by subset moves, Cuntz splice. give counterexamples other not remaining moves. The same results hold if one restricts class strongly connected