SEMINAR: Groups and Combinatorics Seminar: Normal and non-normal Cayley graphs of non-prime power order

Time and place: 16:00 Friday 25 November in LT G16, Robert Street Building

Speaker: Yian Xu (UWA)

Title: Normal and non-normal Cayley graphs of non-prime power order

Abstract: Let Q be a known generalised quadrangle of order (q - 1, q + 1), where q is a prime power p^k with p eq 5. The point graph of Q has order q^3 and is called a BG-graph. In Bamberg and Giudici (2011), the authors proved that a BG-graph is a normal and non-normal Cayley graph for two isomorphic groups. In this paper, we show that the Cayley graphs obtained from a finite number of BG-graphs by Cartesian product, direct product, and strong product respectively also possess this property. In particular, we construct normal and non-normal Cayley graphs of non-prime power order.