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New constructions of non-regular cospectral graphs
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New constructions of non-regular cospectral graphs
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Paper
New constructions of non-regular cospectral graphs
2023
Overview
We consider two types of joins of graphs \\(G_{1}\\) and \\(G_{2}\\), \\(G_{1}\\veebar G_{2}\\) - the Neighbors Splitting Join and \\(G_{1}\\underset{=}{\\lor}G_{2}\\) - the Non Neighbors Splitting Join, and compute the adjacency characteristic polynomial, the Laplacian characteristic polynomial and the signless Laplacian characteristic polynomial of these joins. When \\(G_{1}\\) and \\(G_{2}\\) are regular, we compute the adjacency spectrum, the Laplacian spectrum, the signless Laplacian spectrum of \\(G_{1}\\underset{=}{\\lor}G_{2}\\) and the normalized Laplacian spectrum of \\(G_{1}\\veebar G_{2}\\) and \\(G_{1}\\underset{=}{\\lor}G_{2}\\). We use these results to construct non regular, non isomorphic graphs that are cospectral with respect to the four matrices: adjacency, Laplacian , signless Laplacian and normalized Laplacian.
Publisher
Cornell University Library, arXiv.org
Subject
