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Research Article | Open Access

Distance spectrum of some zero divisor graphs

Fareeha Jamal( ), Muhammad Imran
Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain 15551, Abu Dhabi, UAE
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Abstract

In the present article, we give the distance spectrum of the zero divisor graphs of the commutative rings Zt[x]/⟨x4⟩ ( t is any prime), Zt2[x]/⟨x2⟩ ( t≥3 is any prime) and Ft[u]/⟨u3⟩ ( t is an odd prime), where Zt is an integer modulo ring and Ft is a field. We calculated the inertia of these zero divisor graphs and established several sharp bounds for the distance energy of these graphs.

Keywords

zero divisor graphsdistance energydistance spectrumcommutative rings
CLC number: 05C25, 05C50, 15A18

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 23979-23996
DOI: 10.3934/math.20241166

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Cite this article:
Jamal F, Imran M. Distance spectrum of some zero divisor graphs. AIMS Mathematics, 2024, 9(9): 23979-23996. https://doi.org/10.3934/math.20241166

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Received: 28 May 2024
Revised: 02 July 2024
Accepted: 09 July 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)