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On the (outer)planarity of the intersection graph of idealization | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 تیر 1405 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31194.2777 | ||
| نویسندگان | ||
| Nematollah Shirmohammadi* 1؛ Akram Mahmoodi2؛ Alireza Vahidi2 | ||
| 1Department of Pure Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran | ||
| 2Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity. The intersection graph of ideals of a ring $R$ is an undirected simple graph denoted by $\Gamma(R)$ whose vertices are in a one-to-one correspondence with nonzero proper ideals and two distinct vertices are joined by an edge if and only if the corresponding ideals of $R$ have a nonzero intersection. Let $M$ be a unitary nonzero $R$-module and let $R\ltimes M$ be the idealization of $M$ in $R$. In this paper, we provide a characterization of the planarity of the intersection graph of idealization. We then conclude that the intersection graph of idealization is planar if and only if it is outerplanar. | ||
| کلیدواژهها | ||
| Idealization؛ intersection graph؛ planarity | ||
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