Center of intersection graph of submodules of a module

Abstract

Let R be a commutative ring and M be a unital R-module. The intersection graph of submodules of M, denoted by G M , is the graph whose vertex set is the collection of all submodules of M and in which two distinct vertices A and B are adjacent if and only if A ∩ B ̸ = 0. In this paper the notion of essentiality of modules plays a vital role in the study of intersection graph of submodules of M. This notion gives a new dimension in characterizing the center of intersection graphs of submodules of M. We define mna (maximal non-adjacent) vertex in G M and observe some of its characteristics. The notion of complemented intersection graph exhibits some significant algebraic and graphical properties. Moreover, defining the concept of isolated center in G M we establish certain results related to mna vertex. c