The large sum graph related to comultiplication modules

Abstract

Let $R$ be a commutative ring and $M$ be an $R$-module. We define the large sum graph, denoted by $\acute{G}(M)$, as a graph with the vertex set of non-large submodules of $M$ and two distinct vertices are adjacent if and only if $N+K$ is a non-large submodule of $M$. In this article, we investigate the connection between the graph-theoretic properties of $\acute{G}(M)$ and algebraic properties of $M$ when $M$ is a comultiplication $R$-module.