Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n
The induced subgraph of a unit graph with vertex set as the idempotent elements of a ring R is a graph which is obtained by deleting all non idempotent elements of R. Let C be a subset of the vertex set in a graph Γ. Then C is called a perfect code if for any x, y ∈ C the union of the closed neighbo...
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World Scientific and Engineering Academy and Society
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my.utm.944792022-03-31T15:46:22Z http://eprints.utm.my/id/eprint/94479/ Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n Mudaber, Mohammad Hassan Sarmin, Nor Haniza Gambo, Ibrahim QA Mathematics The induced subgraph of a unit graph with vertex set as the idempotent elements of a ring R is a graph which is obtained by deleting all non idempotent elements of R. Let C be a subset of the vertex set in a graph Γ. Then C is called a perfect code if for any x, y ∈ C the union of the closed neighbourhoods of x and y gives the the vertex set and the intersection of the closed neighbourhoods of x and y gives the empty set. In this paper, the perfect codes in induced subgraphs of the unit graphs associated with the ring of integer modulo n, Zn that has the vertex set as idempotent elements of Zn are determined. The rings of integer modulo n are classified according to their induced subgraphs of the unit graphs that accept a subset of a ring Zn of different sizes as the perfect codes. World Scientific and Engineering Academy and Society 2021-09 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/94479/1/NorHanizaSarmin2021_PerfectCodesOverInduced.pdf Mudaber, Mohammad Hassan and Sarmin, Nor Haniza and Gambo, Ibrahim (2021) Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n. WSEAS Transactions on Mathematics, 20 . pp. 399-403. ISSN 1109-2769 http://dx.doi.org/10.37394/23206.2021.20.41 DOI:10.37394/23206.2021.20.41 |
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QA Mathematics Mudaber, Mohammad Hassan Sarmin, Nor Haniza Gambo, Ibrahim Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n |
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The induced subgraph of a unit graph with vertex set as the idempotent elements of a ring R is a graph which is obtained by deleting all non idempotent elements of R. Let C be a subset of the vertex set in a graph Γ. Then C is called a perfect code if for any x, y ∈ C the union of the closed neighbourhoods of x and y gives the the vertex set and the intersection of the closed neighbourhoods of x and y gives the empty set. In this paper, the perfect codes in induced subgraphs of the unit graphs associated with the ring of integer modulo n, Zn that has the vertex set as idempotent elements of Zn are determined. The rings of integer modulo n are classified according to their induced subgraphs of the unit graphs that accept a subset of a ring Zn of different sizes as the perfect codes. |
format |
Article |
author |
Mudaber, Mohammad Hassan Sarmin, Nor Haniza Gambo, Ibrahim |
author_facet |
Mudaber, Mohammad Hassan Sarmin, Nor Haniza Gambo, Ibrahim |
author_sort |
Mudaber, Mohammad Hassan |
title |
Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n |
title_short |
Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n |
title_full |
Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n |
title_fullStr |
Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n |
title_full_unstemmed |
Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n |
title_sort |
perfect codes over induced subgraphs of unit graphs of ring of integers modulo n |
publisher |
World Scientific and Engineering Academy and Society |
publishDate |
2021 |
url |
http://eprints.utm.my/id/eprint/94479/1/NorHanizaSarmin2021_PerfectCodesOverInduced.pdf http://eprints.utm.my/id/eprint/94479/ http://dx.doi.org/10.37394/23206.2021.20.41 |
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