Department of Mathematics, Universitty of Mazandaran, Babolsar, Iran
10.22080/cjms.2026.30838.1792
Abstract
In this paper, we introduce a new algebraic graph associated with modules, called the $r$-small intersection graph of an $A$-module $T$, denoted by $\Gamma_{r}(T)$. The vertices of $\Gamma_{r}(T)$ are all nonzero submodules of $T$, and two distinct vertices are adjacent if and only if their intersection is an $r$-small submodule of $T$. We investigate how algebraic properties of modules influence graph-theoretic properties of $\Gamma_{r}(T)$. In particular, we study connectedness, diameter, girth, planarity and completeness of $\Gamma_{r}(T)$. Among other results, we show that for certain classes of modules, the graph $\Gamma_{r}(T)$ has diameter at most $2$ and we characterize when $\Gamma_{r}(T)$ is complete or a tree.
Nezhadhoseinian, Y. , & Momeni Kohestani, A. (2026). On r-small intersection graph of modules. Caspian Journal of Mathematical Sciences, 15(2), 322-331. doi: 10.22080/cjms.2026.30838.1792
Nezhadhoseinian, Y., Momeni Kohestani, A. (2026). 'On r-small intersection graph of modules', Caspian Journal of Mathematical Sciences, 15(2), pp. 322-331. doi: 10.22080/cjms.2026.30838.1792
CHICAGO
Y. Nezhadhoseinian and A. Momeni Kohestani, "On r-small intersection graph of modules," Caspian Journal of Mathematical Sciences, 15 2 (2026): 322-331, doi: 10.22080/cjms.2026.30838.1792
VANCOUVER
Nezhadhoseinian, Y., Momeni Kohestani, A. On r-small intersection graph of modules. Caspian Journal of Mathematical Sciences, 2026; 15(2): 322-331. doi: 10.22080/cjms.2026.30838.1792
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