The week's pick
Reseach Article
Total Graphs of Idealization
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 87 - Number 15 |
| Year of Publication: 2014 |
| Authors: D. Eswara Rao, D. Bharathi |
10.5120/15286-3986
|
D. Eswara Rao, D. Bharathi . Total Graphs of Idealization. International Journal of Computer Applications. 87, 15 ( February 2014), 31-34. DOI=10.5120/15286-3986
Abstract
Let R be a commutative ring with Z(R), its set of zero divisors. The total zero divisor graph of R, denoted Z(?(R)) is the undirected (simple) graph with vertices Z(R)*=Z(R)-{0}, the set of nonzero zero divisors of R. and for distinct x, y ? z(R)*, the vertices x and y are adjacent if and only if x + y ? z(R). In this paper prove that let R is commutative ring such that Z(R) is not ideal of R then Z(?(R(+)M)) is connected with diam(Z(?(R(+)M))) = 2 and the sub graphs Z(?(R(+)M)) and Reg(?(R(+)M)) of T(?(R(+)M)) are not disjoint. And also prove that let R be a commutative ring such that Z(R) is not an ideal of R with Z(R(+)M) = Z(R)(+)M and Reg(R(+)M) = Reg(R)(+)M then Z(?(R(+)M)) is connected if and only if Z(?(R) is connected and Reg(?(R(+)M)) is connected if and only if Reg(?(R).
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