Quasi perfect codes in the cartesian product of some graphs

Mane, Smruti (Center for Advanced Studies in Mathematics, Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India.)
Shinde, Neeta (College of Engineering Pune, Maharashtra, India)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications

An important question in the study of quasi-perfect codes is whether such codes can be constructed for all possible lengths n. In this paper, we address this question for specific values of n. First, we investigate the existence of quasi-perfect codes in the Cartesian product of a graph G and a path (or cycle), assuming that G admits a perfect code. Second, we explore quasi-perfect codes in the Cartesian products of two or three cycles, Cm□Cn and Cm□Cn□Cl, as well as in the Cartesian products of two or three paths, Pm□Pn and Pm□Pn□Pl.