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arXiv · 2210.06715

Construction of non-regular $A_\alpha$-cospectral graphs from some join of graphs

Najiya V K·Chithra A V
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Abstract

Cospectral graphs are a fascinating concept in graph theory, where two non-isomorphic graphs possess identical sets of eigenvalues. In this paper, we compute the $A_\alpha$-characteristic polynomial of neighbour and non-neighbour splitting join, neighbour and non-neighbour shadow join, central vertex and edge join and duplicate join of two graphs. In addition, when $\graphene_1$ and $\graphene_2$ are regular, we compute the $A_\alpha$-spectrum of these graphs. As an application, we construct non-regular, non-isomorphic graphs that are $A_\alpha$-cospectral.

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Najiya V K, Chithra A V. 2022-10-13. Construction of non-regular $A_\alpha$-cospectral graphs from some join of graphs. https://arxiv.org/abs/2210.06715

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