Normalized Laplacian spectrum of some generalized subdivision-corona of two regular graphs

TL;DR

This paper derives the normalized Laplacian spectra for certain graph constructions involving regular graphs, enabling the identification of new cospectral graphs and generalizing previous spectral results.

Contribution

It provides explicit formulas for the normalized Laplacian spectra of generalized subdivision-corona graphs of regular graphs, extending existing spectral graph theory results.

Findings

Derived spectra formulas for generalized subdivision-corona graphs

Identified non-regular normalized Laplacian cospectral graphs

Generalized previous spectral results in the literature

Abstract

In this paper, we determine the two normalized Laplacian spectrum of generalized subdivision- vertex corona, subdivision-edge corona for a connected regular graph with an arbitrary reg- ular graph in terms of their normalized Laplacian eigenvalues. Moreover, applying these results, we find some non-regular normaliaed Laplacian cospectral graphs. These results generalize the existing results in [11].