BASIS DAN DIMENSI ATAS PADA GRAF PEMBAGI NOL DARI RING KOMUTATIF
DOI:
https://doi.org/10.552273/jms.v2i1.164Keywords:
Base, Upper Dimension, Zero divisor graph, Commutative ringAbstract
Let be the set of nonzero divisors of the commutative ring . The zero divisor graph of is with the set of vertices , where two distinct vertices and are neighbors if and only if . The value of the upper dimension and the minimum solution set (base) of the zero divisor graph is finite. The steps to find the upper dimensions and base are from the specified ring, determine the zero divisor graph of the ring, and look for a different representation of . The set is called the solution set if all the vertices of have different representations of . In this study, some theorem about upper dimensions and base of the zero divisor graph of the commutative ring are discussed.
References
A. Ardiansyah, “Total k-defisiensi Titik pada Graf Bipartisi Komplit ????????,????”, Skripsi, Jur. Matematika, Universitas Islam Negeri Maulana Malik Ibrahim, Malang, Indonesia, 2015.
Bondy, J. A., & Murty, Graph Theory with Applications. Ontario: Departement of Combinatorics and Optimization, University of Waterloo, 1976.
Chartrand, G. & Lesniak, L. 1986. Graphs and Digraphs Second Edition. California: a Division of Wadsworth, Inc.
D.D. Anderson, M. Naseer, Beck’s coloring of a commutative ring, J. Algebra 159 (1993) 500–517.
D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring
F. Harary, R.A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976) 191–195
G. Chartrand, C. Poisson, P. Zhang, Resolvability and the upper dimension of graphs, Int. J. Comput. Math. Appl. 39 (2000) 19–28.
Herstein,LN (1999). Topic In Algebra, Secon edition , Newyork: John Wiles and Sons
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988) 208–226
Munir,Renaldi.2005.Matematika Diskrit.Bandung.Informatika
P.J. Slater, Leaves of trees, Congr. Number. 14 (1975) 549–559
Rasiman.dkk. 2018. Teori Ring. Semarang. UNIV PGRI Semarang Press
S. Pirzada, M. Aijaz. S.P Redmond, Upper dimension and bases of zero-divisor graphs of commutative rings, AKCE International Journal of Graphs and Combinatorics. 2019
S.Pirzada, M.Aijaz, S.P.Redmond, On upper dimension of graphs and their bases sets, Discrete Mathematics Letters, 3 (2020) 37–43
Soleha. Setyowati, Dian W. A.W Satrio, “Kajian Sifat – Sifat Graf Pembagi-Nol dari Ring Komutatif dengan Elemen Satuan”, Prosiding Seminar Nasional Matematika dan Pendidikan Matematika 2015 ISBN No. 978-979-028-728-0, Surabaya, 2015
