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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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[1] F.H. Abdulqadr, Maximal ideal graph of commutative rings, Iraqi J. Sci. 61(8) (2020) 2070-2076. [2] A.H. Alwan, and A.M. Alhossaini, On dense subsemimodules and prime semimodules, Iraqi J. Sci. 61(6) (2020) 1446-1455. [3] A.H. Alwan and A.M. Alhossaini, Dedekind multiplication semimodules, Iraqi J. Sci. 61(6) (2020) 1488-1497. [4] A.H. Alwan, and A.M. Alhossaini, Endomorphism semirings of Dedekind semimodules, Int. J. Adv. Sci. Technol. 29(4) (2020) 2361-2369. [5] I. Beck, Coloring of a commutative ring, J. of Algebra, 116(1) (1988) 208-226. [6] C. Berge, Farbung von Graphen deren smtliche beziehungsweise deren ungerade Kreise Starr Sind, Wissenschaftliche Zeitschrift, Martin Luther Univ. Halle-Wittenberg, Math.-Naturwiss. Reihe (1961) 114-115. [7] S. David, and M. Richard, Abstract Algebra, U. S. A.: Prentice-Hall Inc., 1991. [8] D. Dolzan, and P. Oblak, The zero-divisor graphs of rings and semirings, Int. J. Algebra Comput. 22(4) (2012), 1250033, 20 pp. [9] S. Ebrahimi Atani, S. Dolati Pish Hesari, and M. Khoramdel, The identity-summand graph of commutative semirings, J. Korean Math. Soc. 51 (2014) 189-202. [10] S. Ebrahimi Atani, S. Dolati Pish Hesari, and M. Khoramdel, and Z.E. Sarvandi, Intersection Graphs of co-ideals of semirings, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(1) (2019) 840-851. [11] S. Foldes and P.L. Hammer, Split graphs, Proc. 8th South-Eastern Conf. Combin.: Graph Theory Comput., 1977, pp. 311-315. [12] C. Gary and L. Linda, Graphs and Digraphs, 2nd ed., Wadsworth and Brook/ Cole, California, 1986. [13] J.S. Golan, Semirings and Their Applications, Kluwer Academic Publishers, Dordrecht, 1999. [14] R. Gupta, S.M.K. Sen, and S. Ghosh, A variation of zero-divisor graphs, Discuss. Math. Gen. Algebra Appl. 35(2) (2015) 159-176. [15] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc, New York, NY, 1998. [16] Y. Katsov, T.G. Nam, and N.X. Tuyen, On subtractive semisimple semirings, Algebra Colloq. 16(3) (2009) 415-426. [17] T.Y. Lam, A First Course in Non-commutative Rings, Graduate Texts in Mathematics, 131, Springer, Berlin-Heidelberg, New York, 1991. [18] P. Nasehpour, Dedekind semidomains, Cornell University, arXiv:1907.07162v1, (2019), Pages (20). [19] M.A. Abdlhusein, Doubly connected bi-domination in graphs, Discrete Math. Algorithm Appl. 13(2) (2021) 2150009. | ||
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