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...

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Main Authors:	Shahabaddin Ebrahimi Atani, Saboura Dolati Pishhesari, Mehdi Khoramdel, Maryam Sedghi
Format:	Article
Language:	English
Published:	Shahid Beheshti University 2018-07-01
Series:	Categories and General Algebraic Structures with Applications
Subjects:	Lattice minimal prime ideal zero-divisor graph total graph
Online Access:	http://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf

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spelling	doaj-471a0e3e52154b8fac8bd4b6f5fe7b6f2020-11-24T21:00:33ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612018-07-0191152750749Total graph of a $0$-distributive latticeShahabaddin Ebrahimi Atani0Saboura Dolati Pishhesari1Mehdi Khoramdel2Maryam Sedghi3Faculty of Mathematical Sciences, University of Guilan, Rasht, IranFaculty of Mathematical Sciences, University of Guilan, Rasht, IranFaculty of Mathematical Sciences, University of Guilan, Rasht, IranFaculty of Mathematical Sciences, University of Guilan, Rasht, IranLet £ 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.http://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdfLatticeminimal prime idealzero-divisor graphtotal graph
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Shahabaddin Ebrahimi Atani Saboura Dolati Pishhesari Mehdi Khoramdel Maryam Sedghi
spellingShingle	Shahabaddin Ebrahimi Atani Saboura Dolati Pishhesari Mehdi Khoramdel Maryam Sedghi Total graph of a $0$-distributive lattice Categories and General Algebraic Structures with Applications Lattice minimal prime ideal zero-divisor graph total graph
author_facet	Shahabaddin Ebrahimi Atani Saboura Dolati Pishhesari Mehdi Khoramdel Maryam Sedghi
author_sort	Shahabaddin Ebrahimi Atani
title	Total graph of a $0$-distributive lattice
title_short	Total graph of a $0$-distributive lattice
title_full	Total graph of a $0$-distributive lattice
title_fullStr	Total graph of a $0$-distributive lattice
title_full_unstemmed	Total graph of a $0$-distributive lattice
title_sort	total graph of a $0$-distributive lattice
publisher	Shahid Beheshti University
series	Categories and General Algebraic Structures with Applications
issn	2345-5853 2345-5861
publishDate	2018-07-01
description	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.
topic	Lattice minimal prime ideal zero-divisor graph total graph
url	http://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf
work_keys_str_mv	AT shahabaddinebrahimiatani totalgraphofa0distributivelattice AT sabouradolatipishhesari totalgraphofa0distributivelattice AT mehdikhoramdel totalgraphofa0distributivelattice AT maryamsedghi totalgraphofa0distributivelattice
_version_	1716779350726017024

Total graph of a $0$-distributive lattice

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