Non-Trivial Subring Perfect Codes in Unit Graph of Boolean Rings


  • Mohammad Hassan Mudaber Universiti Teknologi Malaysia
  • Nor Haniza Sarmin Universiti Teknologi Malaysia
  • Ibrahim Gambo Universiti Teknologi Malaysia



subring, Boolean ring, unit graph, perfect code


The aim of this paper is to investigate the non-trivial subring perfect codes in a unit graph associated with the Boolean rings. We prove a subring perfect code of size , where , in the unit graphs associated with the finite Boolean rings . Moreover, we give a necessary and sufficient condition for a subring of an infinite Boolean ring  to be a perfect code of size infinity in the unit graph.


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