Scalar Product Graphs of Modules

Author(s):

M. Nouri Jouybari , Y. Talebi * , S. Firouzian

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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.

Keywords:

Scalar Product , Graph , Module

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:10 Issue: 1, Summer Autumn 2019
Pages:
75 to 82
https://www.magiran.com/p2156943