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Reseach Article

Total Graphs of Idealization

by D. Eswara Rao, D. Bharathi
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

@article{ 10.5120/15286-3986,
author = { D. Eswara Rao, D. Bharathi },
title = { Total Graphs of Idealization },
journal = { International Journal of Computer Applications },
issue_date = { February 2014 },
volume = { 87 },
number = { 15 },
month = { February },
year = { 2014 },
issn = { 0975-8887 },
pages = { 31-34 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume87/number15/15286-3986/ },
doi = { 10.5120/15286-3986 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:06:01.724635+05:30
%A D. Eswara Rao
%A D. Bharathi
%T Total Graphs of Idealization
%J International Journal of Computer Applications
%@ 0975-8887
%V 87
%N 15
%P 31-34
%D 2014
%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

Keywords

Zerodivisors Total zerodivisor graph of idealization commutative ring connected graph.