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Barman, B., Rajkhowa, K.. (1403). A graph associated with minimal ideals of a ring. فیزیولوژی و بیوتکنولوژی آبزیان, 12(2), 155-163. doi: 10.22124/jart.2024.23365.1467
B. Barman; K. K. Rajkhowa. "A graph associated with minimal ideals of a ring". فیزیولوژی و بیوتکنولوژی آبزیان, 12, 2, 1403, 155-163. doi: 10.22124/jart.2024.23365.1467
Barman, B., Rajkhowa, K.. (1403). 'A graph associated with minimal ideals of a ring', فیزیولوژی و بیوتکنولوژی آبزیان, 12(2), pp. 155-163. doi: 10.22124/jart.2024.23365.1467
Barman, B., Rajkhowa, K.. A graph associated with minimal ideals of a ring. فیزیولوژی و بیوتکنولوژی آبزیان, 1403; 12(2): 155-163. doi: 10.22124/jart.2024.23365.1467

A graph associated with minimal ideals of a ring

Journal of Algebra and Related Topics
دوره 12، شماره 2، فروردین 2025، صفحه 155-163    اصل مقاله (116.29 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2024.23365.1467
نویسندگان
B. Barman1؛ K. K. Rajkhowa* 2
1Department of Mathematics, Cotton University, India
2Department of Mathematics Cotton University, India
چکیده
‎In this paper‎, ‎a new kind of graph is introduced and investigated‎. ‎The minimal ideal graph for a ring $R$ with unity is an undirected graph whose vertex set contains all non-trivial ideals of $R$‎. ‎We denote the graph by $mI(R)$ and the vertex set by $V(mI(R))$‎. ‎Two vertices $P,Q \in V(mI(R))$ are adjacent if a minimal ideal $p$ of $R$ exists with $p\subset P$ and $p \subset Q$‎. ‎We study the correlation of algebraic properties and graph theoretic properties of $mI(R)$‎. ‎In this article‎, ‎connectedness‎, ‎diameter‎, ‎clique number‎, ‎chromatic number‎, ‎regular character‎, ‎cut vertex etc‎. ‎are discussed‎.
کلیدواژه‌ها
minimal ideal؛ artinian ring؛ clique number؛ chromatic number
مراجع
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