Perfect Codes Over Induced Subgraphs of Unit Graphs of Ring of Integers Modulo n

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Abstract: 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, Z_n that has the vertex set as idempotent elements of Z_n 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 Z_n of different sizes as the perfect codes

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 20, 2021, Art. #41

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Mohammad Hassan Mudaber, Nor Haniza Sarmin, Ibrahim Gambo, "Perfect Codes Over Induced Subgraphs of Unit Graphs of Ring of Integers Modulo n," WSEAS Transactions on Mathematics, vol. 20, pp. 399-403, 2021, DOI:10.37394/23206.2021.20.41
Mohammad Hassan Mudaber, Nor Haniza Sarmin, Ibrahim Gambo. Perfect Codes Over Induced Subgraphs of Unit Graphs of Ring of Integers Modulo n. WSEAS Transactions on Mathematics. 2021;20:399-403. 10.37394/23206.2021.20.41
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