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Join coatom element graph of a lattice | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 مهر 1404 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2025.30161.1776 | ||
| نویسندگان | ||
| Shahabaddin Ebrahimi Atani1؛ Mehdi Khoramdel* 2 | ||
| 1Department of Mathematics, University of Guilan | ||
| 2Department of Mathematics, University of Guilan, P.O.Box 1914, Rasht, Iran. | ||
| تاریخ دریافت: 06 مهر 1404، تاریخ پذیرش: 21 مهر 1404 | ||
| چکیده | ||
| Let $\mathcal{L}$ be a bounded distributive lattice. In this paper, we introduce and investigate the join coatom element graph of $\mathcal{L}$, denoted by $\mathbb{CG} (\mathcal{L})$. It is the (undirected) graph with all nontrivial elements of $\mathcal{L}$ as vertices, and for distinct nontrivial elements $a, b \in \mathcal{L}$, the vertices $a$ and $b$ are adjacent if and only if $a \vee b$ is a coatom element of $\mathcal{L}$. The basic properties and possible structures of the graph $\mathbb{CG}(\mathcal{L})$ are investigated. The connectedness, clique number, domination number and independence number of $\mathbb{CG}(\mathcal{L})$ and their relations to algebraic properties of $\mathcal{L}$ are explored. | ||
| کلیدواژه‌ها | ||
| Lattice؛ coatom, join coatom element graph | ||
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آمار تعداد مشاهده مقاله: 2 |
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