Perfect codes in induced subgraph of unit graph associated with some commutative rings

• Main Authors: Mudaber, Mohammad Hassan, Sarmin, Nor Haniza, Gambo, Ibrahim
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2022
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/102666/1/NorHanizaSarmin2022_PerfectCodesinInducedSubgraph.pdf; http://eprints.utm.my/id/eprint/102666/; http://dx.doi.org/10.11113/jurnalteknologi.v84.17982

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.