Join maximal element graph of lattice modules

Let \pounds be a C-lattice and M be a lattice module over \pounds‎. ‎The join maximal element graph \mathbb{G}(M) is a simple‎, ‎undirected graph with all proper non-zero elements of M as vertices‎, ‎and two distinct vertices‎, ‎N and K‎, ‎are adjacent if and only if N\vee K\in Max(M)‎, ‎where Max(M) is the collection of all maximal elements of M‎. ‎In this paper‎, ‎some properties of the graph \mathbb{G}(M) like diameter‎, ‎girth and clique number are investigated‎. ‎Also‎, ‎the interplay between the algebraic properties of M and the properties of those graphs is studied‎.

کلیدواژه ها:

‎Maximal element ، Jacobson radical J_{rad}(M) ، Join maximal element graph \mathbb{G}(M)