Total graph of a 0-distributive lattice
Publish Year: 1397
Type: Journal paper
Language: English
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Document National Code:
JR_CGASAT-9-1_002
Index date: 14 September 2021
Total graph of a 0-distributive lattice abstract
Let £ 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.
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Total graph of a 0-distributive lattice authors
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
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