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Some properties of the essential annihilating-ideal graph of commutative rings | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 8، دوره 8، شماره 4، اسفند 2023، صفحه 715-724 اصل مقاله (380.93 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27827.1365 | ||
| نویسندگان | ||
| Mohd Nazim* 1؛ Nadeem Ur REHMAN2؛ Shabir Ahmad Mir2 | ||
| 1Department of mathematics, Aligarh Muslim University, Aligarh. | ||
| 2Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India | ||
| چکیده | ||
| Let $\mathcal{S}$ be a commutative ring with unity and $A(\mathcal{S})$ denotes the set of annihilating-ideals of $\mathcal{S}$. The essential annihilating-ideal graph of $\mathcal{S}$, denoted by $\mathcal{EG}(\mathcal{S})$, is an undirected graph with $A^*(\mathcal{S})$ as the set of vertices and for distinct $\mathcal{I}, \mathcal{J} \in A^*(\mathcal{S})$, $\mathcal{I} \sim \mathcal{J}$ is an edge if and only if $Ann(\mathcal{IJ}) \leq_e \mathcal{S}$. In this paper, we classify the Artinian rings $\mathcal{S}$ for which $\mathcal{EG}(\mathcal{S})$ is projective. We also discuss the coloring of $\mathcal{EG}(\mathcal{S})$. Moreover, we discuss the domination number of $\mathcal{EG}(\mathcal{S})$. | ||
| کلیدواژهها | ||
| Annihilating-ideal graph؛ Essential annihilating-ideal graph؛ Crosscap of a graph؛ Domination number of a graph | ||
| مراجع | ||
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