WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 20, 2021
Perfect Codes Over Induced Subgraphs of Unit Graphs of Ring of Integers Modulo n
Authors: , ,
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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<sub>n</sub> that has the vertex set as idempotent elements of Z<sub>n</sub> 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<sub>n</sub> of different sizes as the perfect codes
Pages: 399-403
DOI: 10.37394/23206.2021.20.41