| Speaker: David Dolzan Affiliation: University of Ljubljana Time: 14:00 Tuesday, 20 November, 2018 Location: 303-257 |
| The essence of the commutativity relation on a given magma A (i.e., a nonempty set equipped with an inner operation, written as product ab) is captured in its commuting graph. By definition, this is a simple graph whose vertices are all noncentral elements of A and where two distinct vertices a,b are connected if they commute in A, i.e., if ab=ba. In this talk, we shall consider the commuting graphs of matrix algebras. We shall survey the known results on the properties of the commuting graph, mainly those concerning its connectedness and diameter. We shall also look at a few open problems in this area of research. |