Total graph of a 0-distributive lattice

Let £ be a 0-distributive lattice with the least element 0, the greatest element 1, and Z(£) its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by T(G(£)). It is the graph with all elements of £ as vertices, and for distinct x,y∈£, the vertices x and y are adjacent if and only if x∨y∈Z(£). The basic properties of the graph T(G(£)) and its subgraphs are studied. We investigate the properties of the total graph of 0-distributive lattices as diameter, girth, clique number, radius, and the  independence number.