### Abstract:

In this work we will need the basic knowledge of Graph Theory as our background and as we
go along we will state and prove some of the Lattice and Set Theory results. Every graph in
this work is considered as a finite simple graph, in other words, it is finite, undirected, loopless
and without multiple edges. The class of all finite simple graphs will be denoted by I. If G is
graph in I, we use the notation V(G) to denote the set of all vertices in G and the notation
E(G) to denote the set of all the edges in G.