Complement of the zero divisor graph of a lattice

Abstract

In this paper, we determine when I (L))cthe complement of the zero divisor graphI(L)with respect to a semiprime ideal I of a lattice L, is connected and also determine its diameter, radius, centre and girth. Further, a form of Beck's conjecture is proved for I (L)when ω I(L))c 〈 ∞.©2013 Australian Mathematical Publishing Association Inc.