Join coatom element graph of a lattice

Let \mathcal{L} be a bounded distributive lattice. In this paper, we introduce and investigate the join coatom element graph of \mathcal{L}, denoted by \mathbb{CG} (\mathcal{L}). It is the (undirected) graph with all nontrivial elements of \mathcal{L} as vertices, and for distinct nontrivial elements a, b \in \mathcal{L}, the vertices a and b are adjacent if and only if a \vee b is a coatom element of \mathcal{L}. The basic properties and possible structures of the graph \mathbb{CG}(\mathcal{L}) are investigated. The connectedness, clique number, domination number and independence number of \mathbb{CG}(\mathcal{L}) and their relations to algebraic properties of \mathcal{L} are explored.

کلیدواژه ها:

lattice ، coatom ، join coatom element graph