meet-nonessential graph of an artinian lattice

Let $l$ be a lattice with $1$. the meet-nonessential graph $mathbb{mg} (l)$ of $l$ is a graph whose vertices are all nonessential filters of $l$ and two distinct filters $f$ and $g$ are adjacent if and only if $f wedge g$ is a nonessential filter of $l$. the basic properties and possible structures of the graph $mathbb{mg}(l)$ are investigated. the clique number, domination number and independence number of $mathbb{mg}(l)$ and their relations to algebraic properties of $l$ are explored.