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The small intersection graph of filters of a bounded distributive lattice | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 1 - شماره پیاپی 24، فروردین 2023، صفحه 311-326 اصل مقاله (496.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19422.1248 | ||
| نویسندگان | ||
| Shahabaddin Ebrahimi Atani؛ Mehdi Khoramdel* ؛ Maryam Chenari | ||
| Department of Mathematics, University of Guilan, Rasht, Iran | ||
| چکیده | ||
| Let $L$ be a lattice with $1$ and $0$. The small intersection graph of filters of $L$, denoted by $\Gamma(L)$, is defined to be a graph whose vertices are in one to one correspondence with all non-trivial filters of $L$ and two distinct vertices are adjacent if and only if the intersection of corresponding filters of $L$ is a small filter of $L$. In this paper, the basic properties and possible structures of the graph $\Gamma(L)$ are investigated. Moreover, the complemented property, the domination number and the planar property of $\Gamma(L)$ are considered. | ||
| کلیدواژه‌ها | ||
| Lattice؛ small Filter؛ Small intersection graph | ||
| مراجع | ||
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