報告題目：Cubic core-free symmetric m-Cayley graphs
報告摘要： An m-Cayley graph $\Gamma$ over a group G is defined as a graph which admits G as a semi-regular group of automorphisms with m orbits. This generalises the notions of a Cayley graph (where m = 1) and a bi-Cayley graph (where m = 2). The m-Cayley graph $\Gamma $ over G is said to be normal if G is normal in the automorphism group Aut(\Gamma) of $\Gamma$, and core-free if the largest normal subgroup of Aut(\Gamma) contained in G is the identity subgroup.In this talk, we investigate properties of symmetric m-Cayley graphs in the special case of valency 3, and use these properties to develop a computational method for classifying connected cubic core-free symmetric m-Cayley graphs. Using the classification method, we give a new proof of the fact that there are exactly 15 connected cubic core-free symmetric Cayley graphs, two of which are Cayley graphs over non-abelian simple groups. We also show that there are exactly 109 connected cubic core-free symmetric bi-Cayley graphs, 48 of which are bi-Cayley graphs over non-abelian simple groups, and that there are 1; 6; 81; 462 and 3267 connected cubic core-free 1-arc-regular 3-, 4-, 5-, 6- and 7-Cayley graphs, respectively.