A new intersection-graph type for modules

Abstract

Let R be a ring with unity and M a left R-module. We investigate a new graph associated with M called the simple-intersection graph of M, denoted by $G{S}_R(M)$. Our focus is on exploring the relationship between different algebraic properties of M and properties $G{S}_R(M)$, including connectedness, girth and dominating sets. Our results encompass determining the girth and diameter of GSR(M) and providing insights on the clique and domination numbers.

KEYWORDS:

• Clique
• domination number
• girth
• modules
• simple-intersection graph
• submodules

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 05C25
• 05C38
• 05C40
• 05C69