Akademik Veri Yönetim Sistemi
UPB SCIENTIFIC BULLETIN, SERIES A: APPLIED MATHEMATICS AND PHYSICS, cilt.88, sa.2, ss.81-94, 2026 (SCI-Expanded, Scopus)
In this paper, we introduce the notion of the quasi-center of a semigroup. Based on this concept, we define the quasicommuting graph and the extended quasicommuting graph associated with a semigroup. We show that the extended commuting graph of a semigroup is always a subgraph of its extended quasicommuting graph. We further examine the structural properties of the quasicommuting graph for completely simple semigroups, represented as Rees matrix semigroups over a group with sandwich matrix P. Our results demonstrate that, for a completely simple semigroup, the extended quasicommuting graph coincides with its quasicommuting graph, a property that also holds for the corresponding commuting graph. Thus, the commuting graph of a completely simple semigroup is a subgraph of its quasicommuting graph. Consequently, the study extends the theory of commuting graphs of completely simple semigroups to the broader framework of quasicommuting graphs, thereby enriching the understanding of commuting-like relations within these algebraic structures.