@article {
author = {Ebrahimi Atani, Shahabaddin and Dolati Pishhesari, Saboura and Khoramdel, Mehdi and Sedghi, Maryam},
title = {Total graph of a $0$-distributive lattice},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {15-27},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.15},
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.},
keywords = {Lattice,minimal prime ideal,zero-divisor graph,total graph},
url = {https://cgasa.sbu.ac.ir/article_50749.html},
eprint = {https://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf}
}