Meet Atom Element Graph of a Lattice

Let $\mathcal{L}$ be a bounded lattice. The meet atom element graph $\mathbb{AG} (\mathcal{L})$ of $\mathcal{L}$ is a simple undirected graph whose vertices are all nontrivial elements of $\mathcal{L}$ and any two distinct vertices $a$ and $b$ are adjacent if and only if $a \wedge b$ is an atom element of $\mathcal{L}$. The basic properties and possible structures of the graph $\mathbb{AG}(\mathcal{L})$ are investigated. The connectedness, clique number, domination number and independence number of $\mathbb{AG}(\mathcal{L})$ and their relations to algebraic properties of $\mathcal{L}$ are explored.