Signless Laplacian and normalized Laplacian on the H-join operation of graphs

Abstract

In this paper, we consider a generalized join operation, that is, the H-join on graphs, where H is an arbitrary graph. In terms of the signless Laplacian and the normalized Laplacian, we determine the spectra of the graphs obtained by this operation on regular graphs. Some additional consequences on the spectral radius, integral graphs and cospectral graphs, etc. are also obtained.

Signless and normalized Laplacian spectrums of the power graph and its supergraphs of certain finite groups

“…We now state another result of [20] which is crucial in computing normalized Laplacian eigenvalues Γ D2n , P(D 2n ), Γ T4n and P(T 4n ).…”

On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤn

“…The central objective of our research is to conduct a comprehensive analysis of the normalized Laplacian spectra of the weakly zero-divisor graph for a finite commutative ring Z n across various values of n. To achieve this, we use the concept of the normalized Laplacian spectra on the H-join operation of graphs, which was introduced by Wu et al [24].…”

A generalization of Fiedler's lemma and the spectra of H-join of graphs

“…, G k , where the subsets S i (G) ⊂ V (G i ) are arbitrary for 1 ≤ i ≤ k. Also, we deduce the characteristic polynomial of the generalized corona of graphs by visualizing corona as an H-join of graphs. Hence the results obtained (mostly for regular graphs) in [4,5,8,13,16,23,24], are generalized here for any graphs.…”