%0 Journal Article
%T Scalar Product Graphs of Modules
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Nouri Jouybari, M.
%A Talebi, Y.
%A Firouzian, S.
%D 2019
%\ 12/01/2019
%V 10
%N Special Issue ( Nonlinear Analysis in Engineering and Sciences)
%P 75-82
%! Scalar Product Graphs of Modules
%K Scalar Product
%K Graph
%K Module
%R 10.22075/ijnaa.2019.4398
%X 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.
%U https://ijnaa.semnan.ac.ir/article_4398_64d6b7e17ebef0902821a02c189f188e.pdf