Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
For a commutative semiring R with non-zero identity, the graph Ω(R) of R, is the graph whose vertices are all elements of R and two distinct vertices x and y are adjacent if and only if the product of the co-ideals generated by x and y is R. In this paper, we study some properties of this graph such as planarity, domination number and connectivity.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
91--100
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran
autor
- Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran
Bibliografia
- [1] Anderson D.F., Livingston P.S., The zero-divisor graph of a commutative ring, J. Algebra, 217(1999), 434-447.
- [2] Bollobás B., Graph Theory, An Introductory Course, Springer-Verlag, New York, 1979.
- [3] Chaudhari J.N., Ingale K.J., Prime avoidance theorem for co-ideals in semirings, Research J. of Pure Algebra, 1(9)(2011), 213-216.
- [4] Ebrahimi Atani S., The zero-divisor graph with respect to ideals of a commutative semiring, Glas. Math., 43(63)(2008), 309-320.
- [5] Ebrahimi Atani S., Dolati Pish Hesari S., Khoramdel M., Strong co-ideal theory in quotients of semirings, J. of Advanced Research in Pure Math., 5(3)(2013), 19-32.
- [6] Ebrahimi Atani S., Dolati Pish Hesari S., Khoramdel M., A fundamental theorem of co-homomorphisms for semirings, Thai J. Math., 12(2)(2014), 491-497.
- [7] Golan J.S., Semirings and their Applications, Kluwer Academic Publishers Dordrecht, 1999.
- [8] Maimani H.R., Salimi H., Sattari A., Yassemi S., Comaximal graph of commutative rings, J. Algebra, 319(2008), 1801-1808.
- [9] Talebi Y., Darzi A., The generalized total graph of a commutative semiring, Ricerche Mat., 66 (2017), 579-589. DOI:10.1007/s11587-017-0321-4.
- [10] Talebi Y., Darzi A., On graph associated to co-ideals of commutative semirings, Comment. Math. Univ. Carolin., 58(3)(2017), (293-305).
- [11] Wang H., On rational series and rational language, Theor. Comput. Sci., 205(1998), 329-336.
- [12] West D.B., Introduction To Graph Theory, Prentice-Hall of India Pvt. Ltd, 2003.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-87b8432a-df98-4513-badb-1c60d8d9c212