The intersection graph of graded submodules of a graded module

Abstract

In this article, we introduce and study the intersection graph of graded submodules of a graded module. Let MM be a left GG-graded RR-module. We define the intersection graph of GG-graded RR-submodules of MM, denoted by Γ(G,R,M)\Gamma \left(G,R,M), to be a simple undirected graph whose set of vertices consists of all nontrivial GG-graded RR-submodules of MM, where two vertices are adjacent if their intersection is nonzero. We study properties of these graphs, such as connectivity, diameter, and girth. We also investigate the intersection graph of graded submodules for certain types of gradings such as faithful and strong gradings.

Keywords

• graded ring
• graded module
• intersection graph
• submodule
• homogeneous
• 13a02
• 05c25
• 16w50