Mudaber, Mohammad Hassan and Sarmin, Nor Haniza and Gambo, Ibrahim
(2022)
*Perfect codes in induced subgraph of unit graph associated with some commutative rings.*
Jurnal Teknologi, 84
(5).
pp. 131-136.
ISSN 0127-9696

PDF
638kB |

Official URL: http://dx.doi.org/10.11113/jurnalteknologi.v84.179...

## Abstract

The unit graph associated with a ring R is the graph whose vertices are elements of R , and two different vertices x and y are adjacent if and only if x +y∈U R where U(R) is the set of unit elements of .R The aim of this paper is to present the perfect codes in induced subgraph of unit graph associated with some commutative rings with unity in which its vertex set is U(R). UR We characterize some families of commutative rings with induced subgraphs of unit graphs accepting the non-trivial perfect codes, and some other families of commutative rings with induced subgraphs of unit graphs which do not accept perfect codes.

Item Type: | Article |
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Uncontrolled Keywords: | commutative ring, induced subgraph, perfect code, unit graph, unit of ring |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 102666 |

Deposited By: | Yanti Mohd Shah |

Deposited On: | 13 Sep 2023 02:26 |

Last Modified: | 13 Sep 2023 02:26 |

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