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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Main Authors: Mudaber, Mohammad Hassan, Sarmin, Nor Haniza, Gambo, Ibrahim
Format: Article
Language:English
Published: World Scientific and Engineering Academy and Society 2021
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Online Access: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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Institution: Universiti Teknologi Malaysia
Language: English
id my.utm.94479
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spelling 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
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Mudaber, Mohammad Hassan
Sarmin, Nor Haniza
Gambo, Ibrahim
Perfect codes over induced subgraphs of unit graphs of ring of integers modulo n
description 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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