Total graph of a $0$-distributive lattice
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 vert...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
Published: |
Shahid Beheshti University
2018-07-01
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Series: | Categories and General Algebraic Structures with Applications |
Subjects: | |
Online Access: | http://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf |
Summary: | 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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ISSN: | 2345-5853 2345-5861 |