Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach
The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. The topological index is utilized as a significant tool in the study of the quantitative structure activity rel...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2023/6815657 |
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| _version_ | 1832548008146763776 |
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| author | Sourav Mondal Muhammad Imran Nilanjan De Anita Pal |
| author_facet | Sourav Mondal Muhammad Imran Nilanjan De Anita Pal |
| author_sort | Sourav Mondal |
| collection | DOAJ |
| description | The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. The topological index is utilized as a significant tool in the study of the quantitative structure activity relationship (QSAR) and quantitative structures property relationship (QSPR) which correlate a molecular structure to its different properties and activities. Graphs containing finite commutative rings have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this article, the topological indices of the total graph Tℤnn∈ℤ+, the zero divisor graph Γℤrn (r is prime, n∈ℤ+), and the zero divisor graph Γℤr×ℤs×ℤt (r,s,t are primes) are computed using some algebraic polynomials. |
| format | Article |
| id | doaj-art-b4d17621d729485e97abaf9d52547070 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b4d17621d729485e97abaf9d525470702025-02-03T06:42:41ZengWileyComplexity1099-05262023-01-01202310.1155/2023/6815657Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial ApproachSourav Mondal0Muhammad Imran1Nilanjan De2Anita Pal3Department of MathematicsDepartment of Mathematical SciencesDepartment of MathematicsDepartment of MathematicsThe algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. The topological index is utilized as a significant tool in the study of the quantitative structure activity relationship (QSAR) and quantitative structures property relationship (QSPR) which correlate a molecular structure to its different properties and activities. Graphs containing finite commutative rings have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this article, the topological indices of the total graph Tℤnn∈ℤ+, the zero divisor graph Γℤrn (r is prime, n∈ℤ+), and the zero divisor graph Γℤr×ℤs×ℤt (r,s,t are primes) are computed using some algebraic polynomials.http://dx.doi.org/10.1155/2023/6815657 |
| spellingShingle | Sourav Mondal Muhammad Imran Nilanjan De Anita Pal Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach Complexity |
| title | Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach |
| title_full | Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach |
| title_fullStr | Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach |
| title_full_unstemmed | Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach |
| title_short | Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach |
| title_sort | topological indices of total graph and zero divisor graph of commutative ring a polynomial approach |
| url | http://dx.doi.org/10.1155/2023/6815657 |
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