On the line graphs of zero-divisor graphs of posets

Abstract

In this paper, we study the zero-divisor graph [Formula: see text] of a poset [Formula: see text] and its line graph [Formula: see text]. We characterize all posets whose [Formula: see text] are star, finite complete bipartite or finite. Also, we prove that the diameter of [Formula: see text] is at most 3 while its girth is either 3, 4 or [Formula: see text]. We also characterize [Formula: see text] in terms of their diameter and girth. Finally, we classify all posets [Formula: see text] whose [Formula: see text] are planar.