WHEN IDEAL-BASED ZERO-DIVISOR GRAPHS ARE COMPLEMENTED OR UNIQUELY COMPLEMENTED

Year 2017, , 198 - 216, 17.01.2017

Jesse Gerald Smith Jr

https://doi.org/10.24330/ieja.296332

Cited By: 1

Abstract

Let R be a commutative ring with nonzero identity and I a proper
ideal of R. The ideal-based zero-divisor graph of R with respect to the ideal
I, denoted by ΓI (R), is the graph on vertices {x ∈ R \ I | xy ∈ I for some
y ∈ R\I}, where distinct vertices x and y are adjacent if and only if xy ∈ I. In
this paper, we give a complete classification of when an ideal-based zero-divisor
graph of a commutative ring is complemented or uniquely complemented based
on the total quotient ring of R/I.

Keywords

: Zero-divisor graph, ideal-based, complemented graph, uniquely complemented graph

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