TY - JOUR
ID - 50749
TI - Total graph of a $0$-distributive lattice
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Ebrahimi Atani, Shahabaddin
AU - Dolati Pishhesari, Saboura
AU - Khoramdel, Mehdi
AU - Sedghi, Maryam
AD - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Y1 - 2018
PY - 2018
VL - 9
IS - 1
SP - 15
EP - 27
KW - Lattice
KW - minimal prime ideal
KW - zero-divisor graph
KW - total graph
DO - 10.29252/cgasa.9.1.15
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_50749.html
L1 - https://cgasa.sbu.ac.ir/article_50749_c43feee35e55c325b3f13fa98313523d.pdf
ER -