# Properties of Congruence Lattices of Graph Inverse Semigroups

@inproceedings{AnagnostopoulouMerkouri2021PropertiesOC, title={Properties of Congruence Lattices of Graph Inverse Semigroups}, author={Marina Anagnostopoulou-Merkouri and Zachary Mesyan and J. D. Mitchell}, year={2021} }

From any directed graph E one can construct the graph inverse semigroup G ( E ), whose elements, roughly speaking, correspond to paths in E . Wang and Luo showed that the congruence lattice L ( G ( E )) of G ( E ) is upper-semimodular for every graph E , but can fail to be lower-semimodular for some E . We provide a simple characterisation of the graphs E for which L ( G ( E )) is lower-semimodular. We also describe those E such that L ( G ( E )) is atomistic, and characterise the minimal…

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