Identity meet graph of elements of lattices

Articles in Press

Document Type : Research Paper

Author

Department of Pure Mathematics, University of Guilan, Rasht, Iran

Abstract

Let $\mathcal{L}$ be a complete lattice. The identity meet graph of elements of $\mathcal{L}$, denoted by $\mathbb{IMG} (\mathcal{L})$, is an undirected simple graph whose vertices are all nontrivial elements of $\mathcal{L}$ and two distinct elements $x$ and $y$ are adjacent if and only if $x \vee y = 1$ and $x \wedge y \neq 0$. The basic properties and possible structures of the graph $\mathbb{IMG}(\mathcal{L})$ are investigated. The connectedness, clique number, domination number, independence number, chromatic number of $\mathbb{IMG}(\mathcal{L})$ and their relations to algebraic properties of $\mathcal{L}$ are explored.

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Journal of Algebra and Related Topics

Articles in Press, Corrected Proof
Available Online from 19 February 2026

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