Title of article :
Total graph of a 0-distributive lattice
Author/Authors :
Ebrahimi Atani ، Shahabaddin - University of Guilan , Dolati Pishhesari ، Saboura - University of Guilan , Khoramdel ، Mehdi - University of Guilan , Sedghi ، Maryam - University of Guilan
Abstract :
Abstract. 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
Keywords :
Lattice , minimal prime ideal , zero , divisor graph , total graph
Journal title :
Categories and General Algebraic Structures with Applications
Journal title :
Categories and General Algebraic Structures with Applications
