Graphs of BCI/BCK -algebras

The aim of this paper is to study special graphs of BCI/BCK -algebras. In this paper, we introduce onekind of graph of BCI -algebras based on branches of X and two kinds of graphs of BCK -algebras based on ideal I .Then we study some of the essential properties of graph theory on the basis of those structures. In particular, we studythe planar, outerplanar, toroidal, K -connected, chordal, K -partite, and Eulerian properties of graph theory.

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[1] Afkhami M, Ahmadjavaheri KH, Khashyarmanesh K, Parsapour A. On the comaximal graphs associated to a lattice of genus one. In: Abdollahi A, Akbari S, Erfanian A, Kiani D, editors. Proceedings of the 7th Algebraic Combinatorics Conference; 16–17 October 2014. Mashhad, Iran: Ferdowsi University of Mashhad, 2014, pp. 39-43.
[2] Afkhami M, Barati Z, Khashyarmanesh K. A graph associated to a lattice. Ric Mat 2014; 63: 67-78.
[3] Afkhami M, Khashyarmanesh K, Nafar KH. On the generalization of Cayley graphs associated to a lattice. In: Firouzian S, Kiani D, Taghavi Jelodar A, Talebi Rostami Y, editors. Proceedings of the 6th Algebraic Combinatorics Conference; 30–31 October 2013. Babolsar, Iran: University of Mazandaran, 2013, pp. 10-30.
[4] Alizadeh M, Maimani HR, Pournaki MR, Yassemi S. An ideal theoretic approach to complete partite zero-divisor graphs of posets. Math-IPM 2013; 37: 161-180.
[5] Anderson DD, Naseer M. Beck’s coloring of a commutative ring. J Algebra 1993; 159: 500-514.
[6] Anderson DF, Livingston P. The zero-divisor graph of a commutative ring. J Algebra 1999; 217: 434-447.
[7] Bartlett P. The chromatic number. Introduction to Graph Theory 2011; 2011: 1-5.
[8] Beck I. Coloring of commutative rings. J Algebra 1998; 116: 208-226.
[9] Brouwer AE, Haemers WH. Spectra of Graphs. Berlin, Germany: Springer, 2011.
[10] Diestel R. Graph Theory. New York, NY, USA: Springer, 1997.
[11] Farley JD, Schmidt SE. Comparability graphs of lattices. J Pure Appl Algebra 2008; 212: 832-839.
[12] Hahn G, Tardif C. Graph homomorphism: structure and symmetry. In: Hahn G, Sabidussi G, editors. Graph Symmetry. Dordrecht, the Netherlands: Kluwer Academic Publishers, 1997, pp. 107-167.
[13] Imai Y, Iseki K. On axiom systems of propositional calculi. XIV. Proc Jpn Acad 1966; 42: 19-22.
[14] Iseki K. An algebra related with a propositional calculus. Proc Jpn Acad 1966; 42: 26-29.
[15] Iwai S, Ogawa K, Tsuchiya M. Note on construction methods of upper bound graphs. AKCE J Graphs Combin 2004; 1: 103-108.
[16] Iwai S, Ogawa K, Tsuchiya M. A note on chordal bound graphs and posets. Discrete Math 2008; 308: 955-961.
[17] Jun YB, Lee KJ. Graphs based on BCI/BCK-algebras. Int J Math Math Sci 2011; 2011: 616981.
[18] Maimani HR, Pournaki MR, Yassemi S. Zero-divisor graphs with respect to an ideal. Comm Algebra 2006; 34: 923-929.
[19] Meng J, Jun YB. BCK-Algebras. Seoul, South Korea: Kyung Moon Sa Co, 1994.
[20] Mohammadian A, Erfanian A, Farrokhi M. Planar, toroidal and projective generalized Petersen graphs. In: Abdollahi A, Akbari S, Kiani D, editors. Proceedings of the 7th Algebraic Combinatorics Conference; 16–17 October 2014. Mashhad, Iran: Ferdowsi University, 2014, pp. 36-38.
[21] Shahsavar F, Afkhami M, Khashyarmanesh K. On end-regular, planar and outerplanar of zero-divisor graphs of posets. In: Firouzian S, Kiani D, Taghavi Jelodar A, Talebi Rostami Y, editors. Proceedings of the 6th Algebraic Combinatorics Conference; 30–31 October 2013. Babolsar, Iran: University of Mazandaran, 2013, pp. 10-30.
[22] Torkzadeh L, Ahadpanah A, Behzadi M. Graph based on residuated lattices. J Hyperstructures 2014; 3: 27-39.
[23] Xu Y, Ruan D, Qin K, Liu J. Lattice-Valued Logic. Berlin, Germany: Springer-Verlag, 2003.
[24] Yisheng H. BCI-Algebra. Beijing, China: Science Press, 2006.
[25] Zahiri O, Borzooei R. Graph of BCI-algebras. Int J Math Math Sci 2012; 2012: 126835.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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