Meet-nonessential graph of an Artinian lattice

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Mathematical Sciences, Guilan University, Guilan, Iran

Abstract

Let $L$ be a lattice with $1$. The meet-nonessential graph $\mathbb{MG} (L)$ 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 $F \wedge G$ is a nonessential filter of $L$. The basic properties and possible structures of the graph $\mathbb{MG}(L)$ are investigated. The clique number, domination number and independence number of $\mathbb{MG}(L)$ and their relations to algebraic properties of $L$ are explored.
 

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References

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Algebraic Structures and Their Applications
Volume 12, Issue 1
February 2025
Pages 51-63

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