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  1. 641

    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
    “…Motivated by their work, this article investigates the normalized Laplacian spectrum of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><msub><mi mathvariant="double-struck">Z</mi><mi mathvariant="fraktur">n</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> for a more general class of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">n</mi></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">n</mi></semantics></math></inline-formula> is represented as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>p</mi><mn>1</mn><msub><mi>T</mi><mn>1</mn></msub></msubsup><msubsup><mi>p</mi><mn>2</mn><msub><mi>T</mi><mn>2</mn></msub></msubsup></mrow></semantics></math></inline-formula>, with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mn>2</mn></msub></semantics></math></inline-formula> being distinct primes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>p</mi><mn>1</mn></msub><mo><</mo><msub><mi>p</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mn>1</mn></msub><mo>,</mo><msub><mi>T</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> are positive integers.…”
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    Masjid sebagai Agen Baznas: Analisa Potensi SDM Ta’mir Masjid di Kabupaten Jepara by M. Husni Arafat, M. Husni Tamrin, Aan Zainul Anwar, Alex Yusron Al Mufti

    Published 2017-10-01
    Subjects: “…Ta’mir Masjid, Agen Baznas, Zakat Maal, Potensi Zakat…”
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