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.
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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.
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Joshi, V. Zero Divisor Graph of a Poset with Respect to an Ideal. Order 29, 499–506 (2012). https://doi.org/10.1007/s11083-011-9216-2
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DOI: https://doi.org/10.1007/s11083-011-9216-2