Prime Spectrum Graph of C-Lattices

Abstract

Let £ be a C-lattice. Let σ(£) be the set of all prime elements of £ and M(£) be the collection of all maximal elements of £. For S ⊆M(£), we introduce the new graph called S-join graph on σ(£), denoted by Γ_S(σ(£)). We have studied properties like connectivity, diameter and domination number of the graph σ(£) . In this paper, we established that the topological space σ(£) is connected if and only if the graph Γ_S(σ(£)) is connected.