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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Mane, Smruti
Center for Advanced Studies in Mathematics, Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India.
Electrical & Electronics Engineering

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Quasi perfect codes in the cartesian product of some graphs Mane, Smruti; Shinde, Neeta
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.2.14

Abstract

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.
Co-Authors Shinde, Neeta