Malaysian Journal of Mathematical Sciences 16(4): 783–791 (2022) https://doi.org/10.47836/mjms.16.4.10 Malaysian Journal of Mathematical Sciences Journal homepage: https://mjms.upm.edu.my Subset Perfect Codes of Finite Commutative Rings Over Induced Subgraphs of Unit Graphs Mudaber, M. H. 1 , Sarmin, N. H. *1 , and Gambo, I. 2 2 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, , 81310 UTM Johor Bahru, Malaysia 2 Bauchi State University, Gadau, Nigeria E-mail: nhs@utm.my * Corresponding author Received: 6 June 2021 Accepted: 6 October 2022 Abstract The induced subgraph of a unit graph with vertex set as the non unit elements of a ring R is a graph obtained by deleting all unit elements of R. In a graph Γ, a subset of the vertex set is called a perfect code if the balls with radius 1 centred on the subset are pairwise disjoint and their unions yield the whole vertex set. In this paper, we determine the perfect codes of induced subgraphs of the unit graphs associated with some finite commutative rings R with unity that has a vertex set as non unit elements of R. Moreover, we classify the commutative rings in which their associated induced subgraphs of unit graphs admit the trivial and non-trivial perfect codes. We also characterize the commutative rings based on the induced subgraph of unit graphs that do not admit the perfect codes. Furthermore, we prove that the complement induced subgraph of unit graph admit only the trivial subring perfect code. Keywords: Commutative ring; unit graph; induced subgraph; perfect code.