On the eigenvalues of generalized and double generalized stars
Francesco Barioli, Shaun Fallat · Linear and Multilinear Algebra · 2005
We consider describing all possible spectra of symmetric matrices associated with certain graphs by characterizing all possible ordered multiplicity lists. For generalized and double generalized stars we provide a complete description of all possible eigenvalue sequences. This result is obtained by first verifying all possible multiplicity lists for these graphs which, in fact, turns out to be necessary and sufficient for determining all eigenvalue sequences corresponding to these graphs.