﻿ 学术报告-Vertex stabilizers of symmetric graphs and their applications-烟台大学|YanTai University

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A graph, with a group of its automorphism, is said to be transitive, if G is transitive on arcs but not on arcs of the graph. Let X be a connected transitive graph, and let be the vertex stabilizer of a vertex in . In 1980, Djokovic and Miller gave the exact structure of for the cubic case, and Weiss and Potocnik gave such structure for the tetravalent case. In this talk, we will discuss the structure of for the pentavalent and hexavalent cases, and give the idea of the main proof. Also, with the similar method, we can get such structures for the valency 7 and 8. transitive graph is also simply called symmetric graph or arc-transitive graph. A graph is called edge-primitive if the full automorphism group of the graph is primitive on edges. The structure of the vertex stabilizer plays an important role in the study of transitive graph. As we all known that except for a star graph, all the edge-primitive graphs are arc-transitive. We will introduce the method about how to use the structure of to determine the edge-primitive graphs with small valencies, and also some symmetric graphs of certain order and valency. 