Maximal ideal graph of commutative semirings

	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
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
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