Locally distance transitive graphs

Michael Giudici (University of Western Australia, Australia)

A graph is called locally $s$-distance transitive if for each vertex $v$ and positive integer $i\leq s$, the vertex stabiliser $G_v$ acts transitively on the set of vertices at distance $i$ from $v$. This is a generalisation of locally $s$-arc-transitive graphs and also distance transitive graphs. In this talk I will outline recent work with Alice Devillers, Cai Heng Li and Cheryl Praeger that initiates the study of such graphs.