On A Graph Of Submodules

Key Findings & Data: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.

💡

Conclusion & Impact:Moreover, we give connections between the graph-theoretic properties of m(N) and algebraic properties of N.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Non-maximal submodule · connected and copmlete graph

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.

Keywords

Non-maximal submodule connected and copmlete graph

🔖

Cite This Article

Öztürk, A., ÖZEN, T., YILMAZ, E. (2019). On A Graph Of Submodules. Sakarya University Journal of Science, Cilt: 23 Sayı: 3, 396–402. https://ajindex.com/articles/942033

📄 Full Text PDF Viewer

Open in New Tab ↗

↗New Tab

📄

PDF görüntüleyici hazırlanıyor...

References (1)

S. Akbari, H.A. Tavallae and S. Khalashi Gheze-lahmad, “Intersection graphs of submodules of a modules,” J. Algebra and Its Aplications, vol. 11, no. 1, 2012, 1250019.[2] F.W. Anderson and K.R. Fuller, Rings and Cat-egories of Modules, Springer, New York, 1992.[3] J.A. Bandy and U.S.R. Murty, Graph Theory, Springer, New York, 2008.[4] I. Beck, “Coloring of a commutative ring,” J. Algebra, vol. 116, pp. 208-226, 1998.[5] I. Chakrabarty, S. Ghosh, T.K. Mukherjee and M.K. Sen, “Intersection graphs of ideals of rings,” Discrete Math., vol. 309, pp. 5381-5392, 2009. [6] Loft Ali Mahdavi and Yahya Talebi, “Co-intersection graph of submodules of a mod-ule,” Algebra and Discrete Mathematics, vol. 1, pp. 128-143, 2016.[7] E. Yaraneri, “Intersection graphs of modules,” J. Algebra Appl., vol. 12, 2013, 1250218.