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. 399403. ISSN 11092769

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Official URL: http://dx.doi.org/10.37394/23206.2021.20.41
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, 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.
Item Type:  Article 

Uncontrolled Keywords:  perfect code, ring of integer modulo n, unit graph 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  94479 
Deposited By:  Yanti Mohd Shah 
Deposited On:  31 Mar 2022 15:46 
Last Modified:  31 Mar 2022 15:46 
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