PERFECT CODES IN INDUCED SUBGRAPH OF UNIT GRAPH ASSOCIATED WITH SOME COMMUTATIVE RINGS

Authors

  • Mohammad Hassan Mudaber Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Malaysia
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Malaysia https://orcid.org/0000-0003-4291-5746
  • Ibrahim Gambo Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Malaysia https://orcid.org/0000-0003-4405-4492

DOI:

https://doi.org/10.11113/jurnalteknologi.v84.17982

Keywords:

Commutative ring, unit of ring, unit graph, induced subgraph, perfect code

Abstract

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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Published

2022-07-26

How to Cite

Mudaber, M. H. ., Sarmin, N. H., & Gambo, I. (2022). PERFECT CODES IN INDUCED SUBGRAPH OF UNIT GRAPH ASSOCIATED WITH SOME COMMUTATIVE RINGS . Jurnal Teknologi, 84(5). https://doi.org/10.11113/jurnalteknologi.v84.17982

Issue

Section

Science and Engineering