On r-small intersection graph of modules

	On r-small intersection graph of modules
Caspian Journal of Mathematical Sciences
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 اردیبهشت 1405
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2026.30838.1792
نویسندگان
Yasaman Nezhadhoseinian^* ؛ Amirmohammad Momeni Kohestani
Department of Mathematics, Universitty of Mazandaran, Babolsar, Iran
تاریخ دریافت: 29 آذر 1404، تاریخ بازنگری: 15 فروردین 1405، تاریخ پذیرش: 24 فروردین 1405
چکیده
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.
کلیدواژه‌ها
r-small؛ Intersection graph؛ Small submodule

آمار تعداد مشاهده مقاله: 1

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