%0 Journal Article
%T Spectra of Coronae
%A Cam McLeman
%A Erin McNicholas
%J Mathematics
%D 2011
%I arXiv
%R 10.1016/j.laa.2011.02.007
%X We introduce a new invariant, the coronal of a graph, and use it to compute the spectrum of the corona $G\circ H$ of two graphs $G$ and $H$. In particular, we show that this spectrum is completely determined by the spectra of $G$ and $H$ and the coronal of $H$. Previous work has computed the spectrum of a corona only in the case that $H$ is regular. We then explicitly compute the coronals for several families of graphs, including regular graphs, complete $n$-partite graphs, and paths. Finally, we use the corona construction to generate many infinite families of pairs of cospectral graphs.
%U http://arxiv.org/abs/1111.1200v1