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

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 $G_1⊻G_2$, respectively. This paper determines the normalized Laplacian spectra of $G_1\dot{\vee }{G}_2$ and $G_1⊻G_2$ 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 $G_1⊻G_2$ for regular graphs $G_1$ and $G_2$.

15 pages,19 confereces

Cited by in corpus (1)

• Normalized Laplacian spectra of central vertex join and central edge join of graphs