Research Article

Total Graphs of Idealization

by  D. Eswara Rao, D. Bharathi
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 87 - Issue 15
Published: February 2014
Authors: D. Eswara Rao, D. Bharathi
10.5120/15286-3986
PDF

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

                        @article{ 10.5120/15286-3986,
                        author  = { D. Eswara Rao,D. Bharathi },
                        title   = { Total Graphs of Idealization },
                        journal = { International Journal of Computer Applications },
                        year    = { 2014 },
                        volume  = { 87 },
                        number  = { 15 },
                        pages   = { 31-34 },
                        doi     = { 10.5120/15286-3986 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2014
                        %A D. Eswara Rao
                        %A D. Bharathi
                        %T Total Graphs of Idealization%T 
                        %J International Journal of Computer Applications
                        %V 87
                        %N 15
                        %P 31-34
                        %R 10.5120/15286-3986
                        %I Foundation of Computer Science (FCS), NY, USA
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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Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Zerodivisors Total zerodivisor graph of idealization commutative ring connected graph.

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