Total graph of a $0$-distributive lattice | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 3، دوره 9، شماره 1، مهر 2018، صفحه 15-27 اصل مقاله (637.88 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.9.1.15 | ||
| نویسندگان | ||
| Shahabaddin Ebrahimi Atani؛ Saboura Dolati Pishhesari؛ Mehdi Khoramdel* ؛ Maryam Sedghi | ||
| Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Lattice؛ minimal prime ideal؛ zero-divisor graph؛ total graph | ||
| مراجع | ||
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