, Volume 29, Issue 3, pp 499-506
Date: 10 May 2011

Zero Divisor Graph of a Poset with Respect to an Ideal

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Abstract

In this paper, we introduce the zero divisor graph G I (P) of a poset P (with 0) with respect to an ideal I. It is shown that G I (P) is connected with its diameter ≤3, and if G I (P) contains a cycle, then the core K of G I (P) is a union of 3-cycles and 4-cycles. Further, the chromatic number and clique number of G I (P) are shown to be equal. This proves a form of Beck’s conjecture for posets with 0. The complete bipartite zero divisor graphs are characterized.

Dedicated to Professor N. K. Thakare on his 71st birthday.
This research is supported by Board of College and University Development, University of Pune, via the project SC-66.