PERFECT CODES IN INDUCED SUBGRAPH OF UNIT GRAPH ASSOCIATED WITH SOME COMMUTATIVE RINGS
DOI:
https://doi.org/10.11113/jurnalteknologi.v84.17982Keywords:
Commutative ring, unit of ring, unit graph, induced subgraph, perfect codeAbstract
The unit graph associated with a ring is the graph whose vertices are elements of , and two different vertices and are adjacent if and only if where is the set of unit elements of 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 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.
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