Line comaximal graphs

	Line comaximal graphs
Journal of Algebra and Related Topics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 دی 1403
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2025.28997.1732
نویسنده
S. Khojasteh^*
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
چکیده
Let $R$ be a commutative ring with non-zero identity. The comaximal graph is a graph with vertices all elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $Rx +Ry = R$. Let $\Gamma_2(R)$ be the subgraph of the comaximal graph with vertex-set $W^{}(R)$, where $W^{}(R)$ is the set of all non-zero and non-unit elements of $R$. In this paper, we investigate when the graph $\Gamma_2(R)$ is a line graph. We completely present all commutative rings which their comaximal graphs are line graphs. Also, we study when the comaximal graph is the complement of a line graph.
کلیدواژه‌ها
comaximal graph؛ line graph؛ complement of a graph

آمار تعداد مشاهده مقاله: 189

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