International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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Volume 87 - Issue 15 |
Published: February 2014 |
Authors: D. Eswara Rao, D. Bharathi |
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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
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).