SEMINAR: Groups and Combinatorics Seminar, 16:00 17/03/2017 Weatherburn LT: Hui Zhou

Speaker: Hui Zhou (University of Western Australia)

Time and place: 16:00 Friday 17/03/2017 in Weatherburn LT

Title: On top locally-s-distance-transitive graphs

Abstract: A graph with some graph symmetry property is called "top", if it cannot be viewed as a nontrivial normal quotient of some other graph with the same graph symmetry property. Therefore, a graph being top implies that it has no nontrivial normal multicovers, including normal covers. John Conway proved that every s-arc-transitive graph has a nontrivial s-arc-transitive normal cover, so there is no top s-arc-transitive graph. However, there exist top locally-s-distance-transitive graphs, and complete multipartite graphs are examples of this. In this talk, I will give a generic condition (E graphs) for locally-s-distance-transitive graphs to be top, and examples and characterizations of locally-s-distance transitive graphs.