Total graph of a $0$-distributive lattice
نویسندگان
1 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
2 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
3 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
4 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
doi
10.29252/cgasa.9.1.15چکیده
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.
