Generalized Symmetry of Graphs-a Survey

Suohai Fan
Department of Mathematics, Jinan University, Guangzhou 510632, P. R. China


Abstract     Full Text  PDF

Symmetry of graphs has been extensively studied over the past 50 years by using automorphisms of graphs and group theory which have played an important role in graph, and promising and interesting results have been obtained. We introduced generalized symmetry of graphs and investigated it by using endomorphisms of graphs and semigroup theory. In this paper, I will survey some results we have achieved in recent years. The paper consists of the following sections.
1. Introduction;
2. End-regular graphs;
3. End-transitive graphs;
4. Cayley graphs of semigroups;
5. Unretractive graphs;
6. Graphs and their endomorphism monoids.