October 9, 2025Open Access

Some graphs related to submodules of a module

Key Points

The second submodule intersection graph SSI(M) has nonzero proper submodules as vertices, showing distinct adjacency conditions.
In this graph, two submodules are adjacent if one is a second submodule of the other, indicating a novel graph structure.
Additionally, the prime submodule sum graph PSS(M) includes adjacent vertices defined by the prime submodule sum condition.
These concepts provide new insights into the relationships between submodules within R-modules, enhancing the theoretical framework.

Abstract

Let R be a commutative ring with identity and M be an R-module. In this paper, we introduce and investigate the second submodule intersection graph SSI(M) of M with vertices are nonzero proper submodules of M and two distinct vertices N and K are adjacent if and only if is a second submodule of M. Also, we introduce and consider the prime submodule sum graph PSS(M) of M with vertices are non-zero proper submodules of M and two distinct vertices N and K are adjacent if and only if N + K is a prime submodule of M.

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Cite This Study

F. Farshadifar (Wed,) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e018 https://doi.org/https://doi.org/10.48550/arxiv.2505.09448

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