Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58539120180701Total graph of a $0$-distributive lattice15275074910.29252/cgasa.9.1.15ENShahabaddinEbrahimi AtaniFaculty of Mathematical Sciences, University of Guilan, Rasht, IranSabouraDolati PishhesariFaculty of Mathematical Sciences, University of Guilan, Rasht, IranMehdiKhoramdelFaculty of Mathematical Sciences, University of Guilan, Rasht, IranMaryamSedghiFaculty of Mathematical Sciences, University of Guilan, Rasht, IranJournal Article20170127Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, 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 $0$-distributive lattices as diameter, girth, clique number, radius, and the independence number.https://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf