g-Small Intersection Graph of a Module
DOI:
https://doi.org/10.21123/bsj.2024.8967Keywords:
Connectivity, Domination, Module, Small submodule, Small intersection graphAbstract
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.
Received 19/04/2023
Revised 30/07/2023
Accepted 01/08/2023
Published Online First 20/01/2024
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