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Original Articles

A Combinatorial Analysis of Zero-Divisor Graphs on Certain Polynomial Rings

Pages 2040-2047 | Received 04 Aug 2011, Published online: 14 May 2013
 

Abstract

The colouring of zero-divisor graphs on certain quotients of polynomial rings can be effectively studied by virtue of a natural correspondence between the algebraic and the combinatorial structure. Accordingly, in the present paper we revisit a nice counterexample involving the chromatic number of zero-divisor graphs, and provide an alternative proof which mostly relies on a purely combinatorial argument. In the same vein, we generalise the counterexample by altering the initial data and studying some chromatic properties of a finite family of zero-divisor graphs.

2010 Mathematics Subject Classification:

ACKNOWLEDGMENT

The author is grateful to the referees, for their valuable suggestions and remarks.

Notes

Communicated by D. Macpherson.

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