Shahabaddin Ebrahimi Atani - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Saboura Dolati Pishhesari - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Mehdi Khoramdel - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Maryam Sedghi - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Let £ be a ۰-distributive lattice with the least element ۰, the greatest element ۱, and {\rm Z}(£) its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by {\rm T}(G (£)). It is the graph with all elements of £ as vertices, and for distinct x, y \in £, the vertices x and y are adjacent if and only if x \vee y \in {\rm Z}(£). The basic properties of the graph {\rm T}(G (£)) and its subgraphs are studied. We investigate the properties of the total graph of ۰-distributive lattices as diameter, girth, clique number, radius, and the  independence number.

Lattice, minimal prime ideal, zero-divisor graph, total graph