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Characterization and construction of total perfect codes in Semi-Cayley graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 مرداد 1405 اصل مقاله (429.49 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31495.2872 | ||
| نویسندگان | ||
| Masoumeh Koohestani1؛ Doost Ali Mojdeh* 1؛ Mohsen Ghasemi2 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| 2Department of Mathematics, Urmia University, P. O. Box 575615-1818, Urmia, Iran | ||
| چکیده | ||
| In this paper, we investigate the existence and construction of total perfect codes in semi-Cayley graphs. We first establish two equivalent characterizations for their existence: one in terms of a suitable vertex partition and the other through the defining subsets of the graph. These characterizations provide structural criteria for analyzing and constructing such codes. Furthermore, for a vertex subset $T=M_0\cup N_1$, we consider its adjugation, defined by $T^*=M_1\cup N_0$, and prove a necessary and sufficient condition for this operation to preserve the total perfect code property. As an application, we identify a distinguished family of total perfect codes generated from a vertex subset $T$ that is itself a total perfect code. Finally, we unify and extend several previously known results and characterize the relationship between the existence of total perfect codes in semi-Cayley graphs and the property that the graph is a pseudocover of a complete graph. | ||
| کلیدواژهها | ||
| graph partition؛ pseudocover؛ smemi-Cayley graph؛ total perfect code | ||
| مراجع | ||
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