Author/Authors :
Nouri Jouybari, M Department of Mathematics - University of Mazandaran, Babolsar, Iran , Talebi, Y Department of Mathematics - University of Mazandaran, Babolsar, Iran , Firouzian, S Department of Mathematics - Payame Noor University (PNU), Tehran, Iran
Abstract :
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.
