dr. Wilfried Imrich: The distinguishing and endomorphism distinguishing number of graphs and groups

The distinguishing number of graphs was introduced by Albertson and Collins 1996, and has spawned a wealth of results on finite and infinite structures. The idea of the distinguishing number is to break symmetries efficiently, where “symmetries” stands or automorphisms. If one also wishes to break endomorphisms, one arrives at the endomorphism distinguishing number. Although endomorphisms are quite untractable, compared to automorphisms, many interesting results for finite and infinite structures immediately generalize from automorphisms to endomorphisms, and many new and interesting problems arise.