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 non-zero proper submodules of $M$ and two distinct vertices $N$ and $K$ are adjacent if and only if $N \cap K$ 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 $M$.
Farshadifar, F. (2026). Some graphs related to submodules of a module. Caspian Journal of Mathematical Sciences, 15(2), 374-388. doi: 10.22080/cjms.2026.30963.1801
MLA
Faranak Farshadifar. "Some graphs related to submodules of a module", Caspian Journal of Mathematical Sciences, 15, 2, 2026, 374-388. doi: 10.22080/cjms.2026.30963.1801
HARVARD
Farshadifar, F. (2026). 'Some graphs related to submodules of a module', Caspian Journal of Mathematical Sciences, 15(2), pp. 374-388. doi: 10.22080/cjms.2026.30963.1801
CHICAGO
F. Farshadifar, "Some graphs related to submodules of a module," Caspian Journal of Mathematical Sciences, 15 2 (2026): 374-388, doi: 10.22080/cjms.2026.30963.1801
VANCOUVER
Farshadifar, F. Some graphs related to submodules of a module. Caspian Journal of Mathematical Sciences, 2026; 15(2): 374-388. doi: 10.22080/cjms.2026.30963.1801
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