Intersection graphs of co-ideals of semirings
Let R be a semiring with identity. In this paper, we introduce the intersection graph of co-ideals, denoted by G(R). The vertices of G(R) are non-trivial co-ideals of R, and two distinct vertices I and J are adjacent if and only if I∩J≠{1}. The basic properties and possible structures of this graph are studied and the interplay between the algebraic properties of R and the graph-theoretic structure of G(R) is investigated.
Keywords:
Co-ideal, intersection graph, I-semiring,
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- Anderson, D.F., Livingston, P.S., The zero-divisor graph of a commutative rings, J. Algebra, 217 (1999), 434-- 447. Beck, I., Coloring of commutative rings, J. Algebra 116 (1988), 208--226.
- Bondy, J.A., Murty, U.S.R., Graph Theory, Graduate Texts in Mathematics, 244, Springer, New York, 2008.
- Bosak, J., The graphs of semigroups, in Theory of Graphs and its Applications, Academic Press, New York, 1964, pp. 119--125.
- Chakrabarty, I., Ghosh, S., Mukherjee, T. K., Sen, M. K., Intersection graphs of ideals of rings, Discrete Math. 309 (2009), 5381--5392.
- Ebrahimi Atani, S., Dolati Pish Hesari, S., and Khoramdel, M., Strong co-ideal theory in quotients of semirings, J. of Advanced Research in Pure Math., 5(3) (2013), 19--32.
- Ebrahimi Atani, S., Dolati Pish Hesari, S., and Khoramdel, M., The identity-summand graph of commutative semirings, J. Korean Math. Soc., 51 (2014), 189--202.
- Ebrahimi Atani, S., Dolati Pish Hesari, S., and Khoramdel, M., Total graph of a commutative semiring with respect to identity-summand elements, J. Korean Math. Soc. 51(3) (2014), 593-- 607.
- Ebrahimi Atani, S., Dolati Pish Hesari, S., and Khoramdel, M., Total identity-summand graph of a commutative semiring with respect to a co-ideal, J. Korean Math. Soc. 52 (2015), No. 1, pp. 159--176.
- Ebrahimi Atani, S., Dolati Pish Hesari, S., and Khoramdel, M., A co-ideal based identity-summand graph of a commutative semiring, Comment.Math.Univ.Carolin. 56,3 (2015)269--285.
- Ebrahimi Atani, S., Dolati Pish Hesari, S., and Khoramdel, M., A graph associated to proper non-small ideals of a commutative ring, Comment.Math.Univ.Carolin. 58,1 (2017) 1--12.
- Ebrahimi Atani, S., Dolati Pish Hesari, S., and Khoramdel, M., Semisimple semirings with respect to co-ideals theory, Asian-European Journal of Mathematics, 11(3) (2018), (13 pages).
- Golan, J. S., Semirings and their Applications, Kluwer Academic Publisher Dordrecht, 1999.
- Csákány, B., Pollák, G., The graph of subgroups of a finite group, Czechoslovak Math. J. 19 (1969), 241--247.
- Wang, H., On rational series and rational language, Theoret. Comput. Sci. 205 (1998), 329--336.
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi