On Nilpotent Matrices over Bounded Distributive Lattice

In this paper, we study nilpotent matrices over bounded distributive lattice from the point of Graph. We will give some necessary and sufficient conditions for a nilpotent matrix over bounded distributive lattice A: h(A)=m,( h(A)=inf{m|A
^m
=0}), establish some important properties and give a method on how to determine a matrix is a non-nilpotent matrix.