Laplacian and  A_{\alpha}- eigenvalues of unit and total graphs of finite commutative ring

Gayatri Dumka; Prashant  Kushwah

doi:10.26713/cma.v17i3.3623

Authors

Gayatri Dumka Banasthali vidyapith https://orcid.org/0009-0005-4793-637X
Prashant Kushwah Banasthali Vidyapith https://orcid.org/0000-0002-1415-9499

DOI:

https://doi.org/10.26713/cma.v17i3.3623

Keywords:

Laplacian eigenvalues, A_{α} eigenvalues, Commutative ring, Finite local ring

Abstract

This paper examines the spectral characteristics of unit and total graphs associated with finite commutative rings. The A_{\alpha} eigenvalue framework provides a unified approach that unifies the study of classical adjacency spectrum and signless Laplacian spectrum. We establish general results for computing the Laplacian and A_{\alpha} eigenvalues of these graphs, with particular emphasis on finite commutative local rings using the generalized join construction. We derive explicit formulas for the Laplacian and A_{\alpha} spectrum of unit and total graphs of finite commutative rings which allows easy computation of these energies.

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Author Biography

Prashant Kushwah, Banasthali Vidyapith

Professor at Department of Mathematics and Statistics, Banasthali Vidyapith.

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