IJCATR Volume 2 Issue 3

On the Adjacency Matrix and Neighborhood Associated with Zero-divisor Graph for Direct Product of Finite

Kuntala Patra Priyanka Pratim Baruah
10.7753/IJCATR0203.1021
keywords : Zero-divisor, Commutative ring, Adjacency matrix, Neighborhood, Zero-divisor graph, Annihilator.

PDF
The main purpose of this paper is to study the zero-divisor graph for direct product of finite commutative rings. In our present investigation we discuss the zero-divisor graphs for the following direct products: direct product of the ring of integers under addition and multiplication modulo p and the ring of integers under addition and multiplication modulo p2 for a prime number p, direct product of the ring of integers under addition and multiplication modulo p and the ring of integers under addition and multiplication modulo 2p for an odd prime number p and direct product of the ring of integers under addition and multiplication modulo p and the ring of integers under addition and multiplication modulo p2 – 2 for that odd prime p for which p2 – 2 is a prime number. The aim of this paper is to give some new ideas about the neighborhood, the neighborhood number and the adjacency matrix corresponding to zero-divisor graphs for the above mentioned direct products. Finally, we prove some results of annihilators on zero-divisor graph for direct product of A and B for any two commutative rings A and B with unity
@artical{k232013ijcatr02031021,
Title = "On the Adjacency Matrix and Neighborhood Associated with Zero-divisor Graph for Direct Product of Finite ",
Journal ="International Journal of Computer Applications Technology and Research(IJCATR)",
Volume = "2",
Issue ="3",
Pages ="315 - 323",
Year = "2013",
Authors ="Kuntala Patra Priyanka Pratim Baruah"}
  • null