Elsevier

Discrete Mathematics

Volume 338, Issue 3, 6 March 2015, Pages 93-98
Discrete Mathematics

Beck’s conjecture and multiplicative lattices

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Abstract

In this paper, we introduce the multiplicative zero-divisor graph of a multiplicative lattice and study Beck-like coloring of such graphs. Further, it is proved that for such graphs, the chromatic number and the clique number need not be equal. On the other hand, if a multiplicative lattice L is reduced, then the chromatic number and the clique number of the multiplicative zero-divisor graph of L are equal, which extends the result of Behboodi and Rakeei (2011) and Aalipour et al. (2012).

Keywords

Multiplicative zero-divisor graph
Reduced multiplicative lattice
Minimal prime element
n-prime element

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1

The second author gratefully acknowledges the financial support by University Grants Commission, New Delhi, via research project reference number 47-496/12(WRO).