Spectral arbitrariness for trees fails spectacularlyFallat, Shaun M. (Avtor) Hall, H. Tracy (Avtor) Levene, Rupert H. (Avtor) Meyer, Seth A. (Avtor) Nasserasr, Shahla (Avtor) Oblak, Polona (Avtor) Šmigoc, Helena (Avtor) spectrummultiplicity listsrooted treeshedgesinverse eigenvalue problem for graphsGiven a graph G, consider the family of real symmetric matrices with the property that the pattern of their nonzero off-diagonal entries corresponds to the edges of G. For the past 30 years a central problem has been to determine which spectra are realizable in this matrix class. Using combinatorial methods, we identify a family of graphs and multiplicity lists whose realizable spectra are highly restricted. In particular, we construct trees with multiplicity lists that require a unique spectrum, up to shifting and scaling. This represents the most extreme possible failure of spectral arbitrariness for a multiplicity list, and greatly extends all previously known instances of this phenomenon, in which only single linear constraints on the eigenvalues were observed.20242024-08-12 09:48:23Članek v reviji160049sl