The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring
The zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero. This study focuses on determining general formulas for the Szeged index and the Padmakar-Ivan index of the zero-di...
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| Format: | Article |
| Language: | English |
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Universitas Airlangga
2025-03-01
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| Series: | Contemporary Mathematics and Applications (ConMathA) |
| Online Access: | https://e-journal.unair.ac.id/CONMATHA/article/view/63517 |
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| author | Jinan Ambar I Gede Adhitya Wisnu Wardhana Abdurahim |
| author_facet | Jinan Ambar I Gede Adhitya Wisnu Wardhana Abdurahim |
| author_sort | Jinan Ambar |
| collection | DOAJ |
| description | The zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero. This study focuses on determining general formulas for the Szeged index and the Padmakar-Ivan index of the zero-divisor graph for specific commutative rings. The results show that for the first case of ring, the Szeged index is exactly half of the Padmakar-Ivan index. For the second case, the Szeged index is consistently greater than the Padmakar-Ivan index. These findings enhance the understanding of how the algebraic structure of rings influences the topological properties of their associated graphs. |
| format | Article |
| id | doaj-art-4adb01d44ce34c0b88672ca524fc6958 |
| institution | OA Journals |
| issn | 2686-5564 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Universitas Airlangga |
| record_format | Article |
| series | Contemporary Mathematics and Applications (ConMathA) |
| spelling | doaj-art-4adb01d44ce34c0b88672ca524fc69582025-08-20T02:10:57ZengUniversitas AirlanggaContemporary Mathematics and Applications (ConMathA)2686-55642025-03-0171132510.20473/conmatha.v7i1.6351761684The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative RingJinan Ambar0I Gede Adhitya Wisnu Wardhana1Abdurahim2Universitas MataramUniversitas MataramUniversitas MataramThe zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero. This study focuses on determining general formulas for the Szeged index and the Padmakar-Ivan index of the zero-divisor graph for specific commutative rings. The results show that for the first case of ring, the Szeged index is exactly half of the Padmakar-Ivan index. For the second case, the Szeged index is consistently greater than the Padmakar-Ivan index. These findings enhance the understanding of how the algebraic structure of rings influences the topological properties of their associated graphs.https://e-journal.unair.ac.id/CONMATHA/article/view/63517 |
| spellingShingle | Jinan Ambar I Gede Adhitya Wisnu Wardhana Abdurahim The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring Contemporary Mathematics and Applications (ConMathA) |
| title | The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring |
| title_full | The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring |
| title_fullStr | The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring |
| title_full_unstemmed | The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring |
| title_short | The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring |
| title_sort | szeged index and padmakar ivan index on the zero divisor graph of a commutative ring |
| url | https://e-journal.unair.ac.id/CONMATHA/article/view/63517 |
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