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

Mohammad Hassan Mudaber, Nor Haniza Sarmin, Ibrahim Gambo
2021 WSEAS Transactions on 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
more » ... ssociated 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
doi:10.37394/23206.2021.20.41 fatcat:eliot2vfa5cxrlmox64lgwabfy