Thin MC Left Regular Bands*

Left regular bands are a generalisation of semi-lattices where commutativity is removed. In this talk we define a new family of
left regular bands called thin MC left regular bands whose adjacency graph has some nice properties. In particular, we show that its
adjacency graph is an edge labeled graph where every simple cycle has an even number of edges. This talk assumes no knowledge of left
regular bands and is intended for a general mathematical audience.