Abstract

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.

Keywords and Phrases

Diameter, connected graph, complete graph, regular graph, complete bipartite graph.

A.M.S. subject classification

05E30, 05C76, 05C99.

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