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Maximal ideal graph of commutative semirings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 74، دوره 12، شماره 1، مرداد 2021، صفحه 913-926 اصل مقاله (468.1 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4946 | ||
| نویسنده | ||
| Ahmed H. Alwan* | ||
| Department of Mathematics, Faculty of Education for Pure Sciences, Thi-Qar University,Thi-Qar, Iraq | ||
| تاریخ دریافت: 21 دی 1399، تاریخ بازنگری: 12 اسفند 1399، تاریخ پذیرش: 17 اسفند 1399 | ||
| چکیده | ||
| In this paper, a new kind of graph on a commutative semiring is introduced and investigated. The maximal ideal graph of S, denoted by MG(S), is a graph with all nontrivial ideals of S as vertices and two distinct vertices I and J are adjacent if and only if I + J is a maximal ideal of S. In this article, some interrelation between the graph-theoretic properties of this graph and some algebraic properties of semirings are studied. We investigated the basic properties of the maximal ideal graph such as diameter, girth, clique number, cut vertex, and planar property. | ||
| کلیدواژهها | ||
| Semiring؛ Maximal ideal؛ The maximal ideal graph؛ Connectedness؛ Diameter؛ Girth؛ Planar property | ||
| مراجع | ||
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