Payrovi, S. H.Babaei, S.Sengelen Sevim, E.2024-07-182024-07-1820211793-55711793-7183https://doi.org/10.1142/S1793557121501254https://hdl.handle.net/11411/7933Let R be a commutative ring and M be an R-module. The compressed essential graph of M, denoted by EG(M) is a simple undirected graph associated to M whose vertices are classes of torsion elements of M and two distinct classes [m] and [m '] are adjacent if and only if Ann(R)(m) + Ann(R)(m ') is an essential ideal of R. In this paper, we study diameter and girth of EG(M) and we characterize all modules for which the compressed essential graph is connected. Moreover, it is proved that omega(EG(M)) = |Ass(R)(M)|, whenever R is Noetherian and M is a finitely generated multiplication module with r(Ann(R)(M)) = 0.eninfo:eu-repo/semantics/closedAccessZero Divisor GraphEssential Zero Divisor GraphAssociated Prime İdealsZero-Divisor GraphArticle2-s2.0-8509395893710.1142/S17935571215012547Q314N/AWOS:000678604500012