On A Graph of Submodules
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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.
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