Graph based on residuated lattices

Document Type : Research Paper

Authors

1 Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

2 Department of Mathematics, Kerman Science and Research Branch, Islamic Azad University, Kerman, Iran

3 Department of Mathematics,Kerman Science and Research Branch, Islamic Azad University, Kerman, Iran

Abstract

In this paper, the residuated graph of residuated lattices will be studied. To do so, the notion of zero divisors of a nonempty subset of a residuated lattice is first introduced and some related properties are investigated. By means of the set of all zerodivisors of an element of a residuated lattice L, the residuated graph Γ(L) is defined and several examples are given. This graph is connected and also some necessary conditions for the residuated graph to be a star graph are found. Finally, the relation between a residuated lattice L and the residuated graph Γ(L) are studied.

Keywords

References

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Journal of Hyperstructures
Volume 3, Issue 1
June 2014
Pages 27-39

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