Meet-nonessential graph of an Artinian lattice

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Ebrahimi Atani Shahabaddin

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Journal Paper

Paper Information

Journal: ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS Year:2025 | Volume:12 | Issue:1 Page(s): 51-63

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Information Journal Paper

Title

Meet-nonessential graph of an Artinian lattice

Author(s)

Ebrahimi Atani Shahabaddin | Issue Writer Certificate

Keywords

Essential filter

Lattice

Meet-essential graph

Abstract

Let L be a lattice with 1. The meet-nonessential graph MG(L) of L is a graph whose vertices are all nonessential filters of L and two distinct filters F and G are adjacent if and only if F ∧ G is a nonessential filter of L. The basic properties and possible structures of the graph MG(L) are investigated. The clique number, domination number and independence number of MG(L) and their relations to algebraic properties of L are explored.

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