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
Pages
13
From page
15
To page
27
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
Serial Year
2018
Journal title
Categories and General Algebraic Structures with Applications
Record number
2456429
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