主讲人：周三明  教授  澳大利亚墨尔本大学

时  间：2014年11月26日（周三）    16：10-17：10

地  点：必赢76net线路官网北二教学楼516教室

Abstract: A retract of a graph $\Gamma$ is an induced subgraph $\Psi$ of $\Gamma$ such that there exists a homomorphism from $\Gamma$ to $\Psi$ whose restriction to $\Psi$ is the identity map. A graph is  a core if it has no nontrivial retracts. In general, the minimal retracts of a grapare cores and are unique up to isomorphism; they are called the core of the graph. A graph $\Gamma$ is $G$-symmetric if $G$ is a subgroup of the  automorphism group of $\Gamma$ that is transitive on the vertex  set and also transitive on the set of ordered pairs of adjacent vertices. If in addition the vertex set of $\Gamma$ admits a nontrivial partition that is preserved by $G$, then $\Gamma$ is an imprimitive $G$-symmetric graph. We will talk about the cores of imprimitive symmetric graphs of order a product of two distinct primes. In many cases we completely determine the core of such a graph. In other cases we prove that either the graph is a core or its core is isomorphic to one of two graphs, and  further we give conditions on when each of these possibilities occurs.