On A Graph Of Submodules

Abstract

Let S be an assosiative ring with identitiy and N be a right S-module. We define the non-maximal graph m(N) of N with all non-trivial submodules of N as vertices and two distinct vertices A,B are adjecent if and only if A + B is not maximal submodule of N. In this paper, we investigate the connectivity, completeness, girth, domination nuber, cut edges, perfectness and r-partite of m(N). Moreover, we give connections between the graph-theoretic properties of m(N) and algebraic properties of N.