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A note on the zero divisor graph of a lattice | ||
| Transactions on Combinatorics | ||
| مقاله 16، دوره 3، شماره 3، آذر 2014، صفحه 51-59 اصل مقاله (163.32 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.5626 | ||
| نویسندگان | ||
| T. Tamizh Chelvam* ؛ S. Nithya | ||
| Manonmaniam Sundaranar University | ||
| چکیده | ||
| Let $L$ be a lattice with the least element $0$. An element $x\in L$ is a zero divisor if $x\wedge y=0$ for some $y\in L^*=L\setminus \left\{0\right\}$. The set of all zero divisors is denoted by $Z(L)$. We associate a simple graph $\Gamma(L)$ to $L$ with vertex set $Z(L)^*=Z(L)\setminus \left\{0\right\}$, the set of non-zero zero divisors of $L$ and distinct $x,y\in Z(L)^*$ are adjacent if and only if $x\wedge y=0$. In this paper, we obtain certain properties and diameter and girth of the zero divisor graph $\Gamma(L)$. Also we find a dominating set and the domination number of the zero divisor graph $\Gamma(L)$. | ||
| کلیدواژه‌ها | ||
| zero divisor graph؛ lattice؛ atomic lattice؛ ideal؛ dominating set | ||
| مراجع | ||
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