Zero-divisor graphs of lower dismantlable lattices-II
  In this paper, we continue our study of the zero-divisor graphs of lower dismantlable lattices that was started in [20]. 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. 
Avinash Patil, B. N. Waphare and Vinayak Joshi
math.CO