Spectra of coronae
By Cam McLeman, Erin McNicholas. 2011
136 citations recorded by the source corpus.
Abstract We introduce a new invariant, the coronal of a graph, and use it to compute the spectrum of the corona G ∘ 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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry
View Paper: https://www.semanticscholar.org/paper/96796c80707068aeb464f26ebb23ea2b999a915d
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In Computational Theory and Mathematics
In Geometry and Topology
In Organic Chemistry
Citations in the corpus
- Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae (2012, background): “The M -coronal ΓM (x) of an n × n square matrix M is defined [3,16] to be the sum of the entries of the matrix (xIn −M)−1, that is, ΓM (x) = 1 T n (xIn −M)1n, where 1n denotes the column vector of size n with all the entries equal one.”
- Spectra of graph operations based on R-graph (2015, background): “Then [11] A(K p,q )(x) = (p + q)x + 2pq x2 − pq .”
- Spectra of the neighbourhood corona of two graphs (2012, methodology): “In [5,7], many infinite families of pairs of A-cospectral graphs are generated by using the corona construction.”
- The signless Laplacian spectra of the corona and edge corona of two graphs (2013, background): “Next we give an alternative proof of the above theorem by an idea from [8].”