Title：A class of symmetric graphs with 2-arc transitive quotients

Abstract：A graph X is G-symmetric if X admits G as a group of automorphisms acting transitively on the set of vertices and on the set of arcs of X, where an arc is an ordered pair of adjacent vertices. In the case when G is imprimitive on the vertex set V(X) of X, namely when V(X) admits  a nontrivial G-invariant partition B, the quotient graph X_B of X  is always G-symmetric. We obtain necessary conditions for X_B to be (G, 2)-arc transitive  in the case when v-k is an odd prime p, where v is the block size of B and k is the number of vertices in a block having neighbours in a fixed adjacent block.  We prove further that if p=3 or 5 then these necessary conditions are essentially sufficient for X_B to be (G, 2)-arc transitive.

Speaker：Guangjun Xu，Zunyi Normal Unveristy, reviewer of 《Discrete Mathematics》、《Discrete Applied Mathematics》 and《Information Processing Letters》。Xu got his Ph.D from University of Melbourne, his research interest is graph theory.

Date：3:40pm-5:00pm 2021-3-22日（Monday）.

Tencent Meeting ID： 163 506 159

Organizer：School of Mathematical Science

Students and teachers who are interested in graph theory are welcome.

Inviter：Qiang Sun