g-Small Intersection Graph of a Module
Let be a commutative ring with identity, and be a left -module. The g-small intersection graph of non-trivial submodules of , indicated by , is a simple undirected graph whose vertices are in one-to-one correspondence with all non-trivial submodules of and two distinct vertices are adjacent if a...
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| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad, College of Science for Women
2024-08-01
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| Series: | مجلة بغداد للعلوم |
| Subjects: | |
| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8967 |
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| Summary: | Let be a commutative ring with identity, and be a left -module. The g-small intersection graph of non-trivial submodules of , indicated by , is a simple undirected graph whose vertices are in one-to-one correspondence with all non-trivial submodules of and two distinct vertices are adjacent if and only if the intersection of the corresponding submodules is a g-small submodule of . In this article, the interplay among the algebraic properties of , and the graph properties of are studied. Properties of such as connectedness, and completeness are considered. Besides, the girth and the diameter of are determined, as well as presenting a formula to compute the clique and domination numbers of . The graph is complete if, is a generalized hollow module or is a direct sum of two simple modules, is proved.
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| ISSN: | 2078-8665 2411-7986 |