SOME RESULTS ON ATOMI GRAPH OF THE LATTICES

This paper deals with an atomi graph of the finite lattices. Let $L$ be a finite lattice with one atom denoted by $L_a$ and $A(L_a)= \{ x |$ there exist $y \in L_a$ such that $x \wedge y=a$, and $x, y\neq a$, $a$ is an atom of the lattice\}. We defined a relation $x \wedge y=a,$ and $x,y\neq a$ as the atomi of the lattice $L_a$. The atomi graph of the lattice $L_a$, is denoted by $\gamma(L_a)$, is a graph with the vertex set $A(L_a)$ and two distinct vertices $x, y \in A(L_a)$ are adjacent if and only if they are atomi. We study some properties of atomi graph of the lattices.