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arXiv · 1703.06595

On the normalized Laplacian spectra of some subdivision joins of two graphs

Gui-xian Tian·Shu-Yu Cui
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Abstract

For two simple graphs $G_1$ and $G_2$, we denote the subdivision-vertex join and subdivision-edge join of $G_1$ and $G_2$ by $G_1\dot{\vee}G_2$ and $G_1\veebar G_2$, respectively. This paper determines the normalized Laplacian spectra of $G_1\dot{\vee}G_2$ and $G_1\veebar G_2$ in terms of these of $G_1$ and $G_2$ whenever $G_1$ and $G_2$ are regular. As applications, we construct some non-regular normalized Laplacian cospectral graphs. Besides we also compute the number of spanning trees and the degree-Kirchhoff index of $G_1\dot{\vee}G_2$ and $G_1\veebar G_2$ for regular graphs $G_1$ and $G_2$.

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Gui-xian Tian, Shu-Yu Cui. 2017-03-20. On the normalized Laplacian spectra of some subdivision joins of two graphs. https://arxiv.org/abs/1703.06595

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