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arXiv · 1709.02687

The normalized Laplacian spectra of the double corona based on $R$-graph

Ping-Kang Yu·Gui-Xian Tian
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Abstract

For simple graphs $G$, $G_1$ and $G_2$, we denote their double corona based on $R$-graph by $G^{(R)}\otimes{\{G_1,G_2\}}$. This paper determines the normalized Laplacian spectrum of $G^{(R)}\otimes{\{G_1,G_2\}}$ in terms of these of $G$, $G_1$ and $G_2$ whenever $G$, $G_1$ and $G_2$ are regular. The obtained result reduces to the normalized Laplacian spectra of the $R$-vertex corona $G^{(R)}\odot{G_1}$ and $R$-edge corona $G^{(R)}\circleddash{G_2}$ by choosing $G_2$ or $G_1$ as a null-graph, respectively. Finally, applying the results of the paper, we construct infinitely many pairs of normalized Laplacian cospectral graphs.

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Ping-Kang Yu, Gui-Xian Tian. 2017-09-08. The normalized Laplacian spectra of the double corona based on $R$-graph. https://arxiv.org/abs/1709.02687

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