Spectra of Coronae

Details Spectra of Coronae Spectra of Coronae

2011-11-04

arxiv.org/abs/1111.1200v1

Linear Algebra and its Applications, Volume 435, no. 5, (2011)

Mathematics

Combinatorics

9 pages

Scientific paper

10.1016/j.laa.2011.02.007

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.

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