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On the Annihilating and Annihilator-Ideal Graphs of a Lie Algebra | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 شهریور 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.31241.1818 | ||
| نویسندگان | ||
| Shiroyeh Payrovi* 1؛ Yasaman Sadatrasul2 | ||
| 1Department of Mathematics, Imam Khomeini International University, Qazvin, Iran | ||
| 2Department of Mathematics, Imam Khomeini International University, Qazvin, Iran | ||
| تاریخ دریافت: 20 بهمن 1404، تاریخ بازنگری: 15 مرداد 1405، تاریخ پذیرش: 16 مرداد 1405 | ||
| چکیده | ||
| In this article, we define annihilating-ideal graph and annihilator- ideal graph for a Lie algebra. Let $L$ be a Lie algebra over a field $F$ and let $\mathcal{I}(L)$ denote the set of ideals of $L$. The annihilating-ideal graph of $L$, denoted by $AG(L)$, is a graph with vertex set $\mathcal{I}^*(L)=\mathcal{I}(L)\setminus \{I : I\subseteq Z(L)\ \text{or}\ C_L(I)=Z(L)\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $[I,J]=0$. The annihilator-ideal graph of $L$, denoted by $A_I(L)$, is a graph with vertex set $\mathcal{I}(L)^*$ and two distinct vertices $I$ and $J$ are adjacent if and only if $C_L([I,J])\neq C_L(I)\cup C_L(J)$. We study some properties of $AG(L)$ and $A_I(L)$ such as connectivity and diameter. Moreover, we investigate the situations that two graphs $AG(L)$ and $A_I(L)$ are equal. | ||
| کلیدواژهها | ||
| Lie algebra؛ Annihilating-ideal graph؛ Annihilator-ideal graph؛ 2-absorbing ideal | ||
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آمار تعداد مشاهده مقاله: 3 |
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