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In this paper, we continue our study of the zero-divisor graphs of lower dismantlable lattices that was started in [PATIL, A.—WAPHARE, B. N.—JOSHI, V.—POURALI, H. Y.:  Zero-divisor graphs of lower dismantlable lattices I , Math. Slovaca  67  (2017), 285–296]. The present paper mainly deals with an Isomorphism Problem for the zero-divisor graphs of lattices. In fact, we prove that the zero-divisor graphs of lower dismantlable lattices with the greatest element 1 as join-reducible are isomorphic if and only if the lattices are isomorphic.

Zero-divisor graphs of lower dismantlable lattices II