Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682210Special Issue ( Nonlinear Analysis in Engineering and Sciences)20191201Scalar Product Graphs of Modules7582439810.22075/ijnaa.2019.4398ENM.Nouri JouybariDepartment of Mathematics, University of Mazandaran, Babolsar, IranY.TalebiDepartment of Mathematics, University of Mazandaran, Babolsar, IranS.FirouzianDepartment of Mathematics, Payame Noor University (PNU), Tehran, IranJournal Article20200516Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of these graphs is weakly perfect.https://ijnaa.semnan.ac.ir/article_4398_64d6b7e17ebef0902821a02c189f188e.pdf