Total graph of a $0$-distributive lattice
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ID: 46030
2018
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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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atani2018totalcategories
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| Authors | Atani, Shahabaddin Ebrahimi;Pishhesari, Saboura Dolati;Khoramdel, Mehdi;Sedghi, Maryam; |
| Journal | categories and general algebraic structures with applications |
| Year | 2018 |
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