University of Mohaghegh Ardabili Journal of Hyperstructures 2251-8436 3 1 2014 06 01 Graph based on residuated lattices 27 39 2571 10.22098/jhs.2014.2571 EN L. Torkzadeh Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran A. Ahadpanh Department of Mathematics, Kerman Science and Research Branch, Islamic Azad University, Kerman, Iran M. Behzadi Department of Mathematics,Kerman Science and Research Branch, Islamic Azad University, Kerman, Iran Journal Article 2013 09 11 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. https://jhs.uma.ac.ir/article_2571_e0401300b9fee71724de396774e29162.pdf