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.
Nouri Jouybari,M , Talebi,Y and Firouzian,S . (2019). Scalar Product Graphs of Modules. International Journal of Nonlinear Analysis and Applications, 10(Special Issue ( Nonlinear Analysis in Engineering and Sciences)), 75-82. doi: 10.22075/ijnaa.2019.4398
MLA
Nouri Jouybari,M , , Talebi,Y , and Firouzian,S . "Scalar Product Graphs of Modules", International Journal of Nonlinear Analysis and Applications, 10, Special Issue ( Nonlinear Analysis in Engineering and Sciences), 2019, 75-82. doi: 10.22075/ijnaa.2019.4398
HARVARD
Nouri Jouybari M, Talebi Y, Firouzian S. (2019). 'Scalar Product Graphs of Modules', International Journal of Nonlinear Analysis and Applications, 10(Special Issue ( Nonlinear Analysis in Engineering and Sciences)), pp. 75-82. doi: 10.22075/ijnaa.2019.4398
CHICAGO
M Nouri Jouybari, Y Talebi and S Firouzian, "Scalar Product Graphs of Modules," International Journal of Nonlinear Analysis and Applications, 10 Special Issue ( Nonlinear Analysis in Engineering and Sciences) (2019): 75-82, doi: 10.22075/ijnaa.2019.4398
VANCOUVER
Nouri Jouybari M, Talebi Y, Firouzian S. Scalar Product Graphs of Modules. IJNAA. 2019;10(Special Issue ( Nonlinear Analysis in Engineering and Sciences)):75-82. doi: 10.22075/ijnaa.2019.4398
International Journal of Nonlinear Analysis and Applications