Stellenbosch University
Congruence lattices of graphs
Klarise Marais\(^*\) and Andrew
Craig, University of Johannesburg
SAMS Subject Classification Number: 34
Congruence lattices of algebras are widely used to study their corresponding algebra. In this talk we consider a recent extension of the concept of congruences to graphs, developed by Broere, Heidema and Pretorius [1], and extended to graphs with loops by Broere, Heidema and Veldsman [2]. We study lattice-theoretic properties of these congruence lattices, such as distributivity and modularity. We show that congruence lattices of graphs with three or more vertices are all non-distributive. Further, we investigate conditions for modularity and other connections between graphs and their congruence lattices.
References
[1] I. Broere, J. Heidema and L.M. Pretorius, Graph congruences and what they connote, Quaest. Math. 41 (2018), 1045–1058.
[2] I. Broere, J. Heidema and S. Veldsman, Congruences and Hoehnke Radicals on Graphs, Discuss. Math. Graph Theory 40 (2020), 1067–1084.
