Join coatom element graph of a lattice

Document Type : Research Articles

Authors

1 Department of Mathematics, University of Guilan

2 Department of Mathematics, University of Guilan, P.O.Box 1914, Rasht, Iran.

10.22080/cjms.2025.30161.1776

Abstract

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.

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