On A Graph Of Submodules

Yıl 2019, Cilt: 23 Sayı: 3, 396 - 402, 01.06.2019

Ali Öztürk , Tahire Özen , Erol Yılmaz

https://doi.org/10.16984/saufenbilder.483138

Öz

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.

Anahtar Kelimeler

Non-maximal submodule, connected and copmlete graph

Kaynakça

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