Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2
Let S=ℤℊ3×ℤI1I2 be a commutative ring where ℊ,I1 and I2 are positive prime integers with I1≠I2. The zero-divisor graph assigned to S is an undirected graph, denoted as YS with vertex set V(Y(S)) consisting of all Zero-divisor of the ring S and for any c, d ∈V(Y (S)), cd∈EYS if and only if cd =0. A t...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2046173 |
| _version_ | 1811181727700221952 |
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| author | Yonghong Liu Abdul Rauf null AdnanAslam Saira Ishaq Abudulai Issa |
| author_facet | Yonghong Liu Abdul Rauf null AdnanAslam Saira Ishaq Abudulai Issa |
| author_sort | Yonghong Liu |
| collection | DOAJ |
| description | Let S=ℤℊ3×ℤI1I2 be a commutative ring where ℊ,I1 and I2 are positive prime integers with I1≠I2. The zero-divisor graph assigned to S is an undirected graph, denoted as YS with vertex set V(Y(S)) consisting of all Zero-divisor of the ring S and for any c, d ∈V(Y (S)), cd∈EYS if and only if cd =0. A topological index/descriptor is described as a topological-invariant quantity that transforms a molecular graph into a mathematical real number. In this paper, we have computed distance-based polynomials of YR i-e Hosoya polynomial, Harary polynomial, and the topological indices related to these polynomials namely Wiener index, and Hyper-Wiener index. |
| first_indexed | 2024-04-11T09:22:17Z |
| format | Article |
| id | doaj.art-31349b2cdba9472cb49b38bb624b2be9 |
| institution | Directory Open Access Journal |
| issn | 2314-8888 |
| language | English |
| last_indexed | 2024-04-11T09:22:17Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj.art-31349b2cdba9472cb49b38bb624b2be92022-12-22T04:32:09ZengHindawi LimitedJournal of Function Spaces2314-88882022-01-01202210.1155/2022/2046173Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2Yonghong Liu0Abdul Rauf1null AdnanAslam2Saira Ishaq3Abudulai Issa4School of Computer ScienceDepartment of MathematicsDepartment of Natural Sciences and HumanitiesDepartment of MathematicsDepartment of MathematicsLet S=ℤℊ3×ℤI1I2 be a commutative ring where ℊ,I1 and I2 are positive prime integers with I1≠I2. The zero-divisor graph assigned to S is an undirected graph, denoted as YS with vertex set V(Y(S)) consisting of all Zero-divisor of the ring S and for any c, d ∈V(Y (S)), cd∈EYS if and only if cd =0. A topological index/descriptor is described as a topological-invariant quantity that transforms a molecular graph into a mathematical real number. In this paper, we have computed distance-based polynomials of YR i-e Hosoya polynomial, Harary polynomial, and the topological indices related to these polynomials namely Wiener index, and Hyper-Wiener index.http://dx.doi.org/10.1155/2022/2046173 |
| spellingShingle | Yonghong Liu Abdul Rauf null AdnanAslam Saira Ishaq Abudulai Issa Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2 Journal of Function Spaces |
| title | Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2 |
| title_full | Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2 |
| title_fullStr | Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2 |
| title_full_unstemmed | Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2 |
| title_short | Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤℊ3×ℤI1I2 |
| title_sort | computing wiener and hyper wiener indices of zero divisor graph of zg3 zi1i2 |
| url | http://dx.doi.org/10.1155/2022/2046173 |
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