On A Graph of Submodules

Özet

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