Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices
Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography...
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MDPI AG
2018-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/6/12/301 |
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| author | Kashif Elahi Ali Ahmad Roslan Hasni |
| author_facet | Kashif Elahi Ali Ahmad Roslan Hasni |
| author_sort | Kashif Elahi |
| collection | DOAJ |
| description | Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="double-struck">Z</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> <mo>×</mo> <msub> <mi mathvariant="double-struck">Z</mi> <mi>q</mi> </msub> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula>, and <i>q</i> are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutative rings <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="double-struck">Z</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> <mo>×</mo> <msub> <mi mathvariant="double-struck">Z</mi> <mi>q</mi> </msub> </mrow> </semantics> </math> </inline-formula>. |
| first_indexed | 2024-12-21T23:04:20Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T23:04:20Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e8bd9b5140df4dc7b9f6cb00d5d1c8532022-12-21T18:47:14ZengMDPI AGMathematics2227-73902018-12-0161230110.3390/math6120301math6120301Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological IndicesKashif Elahi0Ali Ahmad1Roslan Hasni2Deanship of E-learning and Information Technology, Jazan University, Jazan 45142, Saudi ArabiaCollege of Computer Science and Information Technology, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Mathematics, University Malaysia Terengganu, Kuala Terengganu 21030, Terengganu, MalaysiaChemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="double-struck">Z</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> <mo>×</mo> <msub> <mi mathvariant="double-struck">Z</mi> <mi>q</mi> </msub> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </semantics> </math> </inline-formula>, and <i>q</i> are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutative rings <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="double-struck">Z</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> <mo>×</mo> <msub> <mi mathvariant="double-struck">Z</mi> <mi>q</mi> </msub> </mrow> </semantics> </math> </inline-formula>.https://www.mdpi.com/2227-7390/6/12/301topological indexzero divisor graphscommutative ring |
| spellingShingle | Kashif Elahi Ali Ahmad Roslan Hasni Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices Mathematics topological index zero divisor graphs commutative ring |
| title | Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices |
| title_full | Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices |
| title_fullStr | Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices |
| title_full_unstemmed | Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices |
| title_short | Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices |
| title_sort | construction algorithm for zero divisor graphs of finite commutative rings and their vertex based eccentric topological indices |
| topic | topological index zero divisor graphs commutative ring |
| url | https://www.mdpi.com/2227-7390/6/12/301 |
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