Scalar Product Graphs of Modules

Document Type : Special issue editorial


1 Department of Mathematics, University of Mazandaran, Babolsar, Iran

2 Department of Mathematics, Payame Noor University (PNU), Tehran, Iran



Let 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.