Meet-maximal filter graph of a lattice

Articles in Press

Document Type : Research Paper

Authors

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

10.22034/as.2026.23878.1845

Abstract

In this paper, we introduce and investigate the meet-maximal filter graph of a bounded lattice. It is the (undirected) graph with all nontrivial filters as vertices, and two distinct vertices are adjacent if and only if their meet is a maximal filter. The basic properties and possible structures of the meet-maximal filter graph are investigated. Also, connectedness, clique number, split character, planarity and domination number of meet-maximal filter graph and their relations to algebraic properties of lattices are explored.

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References

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Algebraic Structures and Their Applications

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Available Online from 25 September 2026

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