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    On the Normalized Laplacian Spectrum of the Zero-Divisor Graph of the Commutative Ring <inline-formula><math display="inline"><semantics><msub><mstyle mathvariant="bold"><mi mathvariant="double-struck">Z</mi></mstyle><mrow><msubsup><mi mathvariant="bold-italic">p</mi><mn mathvariant="bold">1</mn><msub><mi mathvariant="bold-italic">T</mi><mn mathvariant="bold">1</mn></msub></msubsup><msubsup><mi mathvariant="bold-italic">p</mi><mn mathvariant="bold">2</mn><msub><mi mathvariant="bold-italic">T</mi><mn mathvariant="bold">2</mn></msub></msubsup></mrow></msub></semantics></math></inline-formula> by Ali Al Khabyah, Nazim, Nadeem Ur Rehman

    Published 2025-01-01
    “…The zero-divisor graph of a commutative ring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">R</mi></semantics></math></inline-formula> with a nonzero identity, denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><mi mathvariant="fraktur">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>, is an undirected graph where the vertex set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><msup><mrow><mo>(</mo><mi mathvariant="fraktur">R</mi><mo>)</mo></mrow><mo>*</mo></msup></mrow></semantics></math></inline-formula> consists of all nonzero zero-divisors of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">R</mi></semantics></math></inline-formula>. …”
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