CAJ | 학술논문

试图对6度1-正则Cayley 图给一个完全分类。利用无核的概念将图自同构群归结到对称群S6的子群。然后根据1-正则图的性质构造出所有可能的具有非交换点稳定子群的无核6度1-正则Cayley图，进一步证明了构造出的图都是有核的，由此给出了这一类图的一个完全分类。
시도대6도1-정칙Cayley 도급일개완전분류。이용무핵적개념장도자동구군귀결도대칭군S6적자군。연후근거1-정칙도적성질구조출소유가능적구유비교환점은정자군적무핵6도1-정칙Cayley도，진일보증명료구조출적도도시유핵적，유차급출료저일류도적일개완전분류。
This paper is trying to give a complete classification of 1-regular Cayley graphs of valency 6. By the definition of core-free, this paper reduces the graph automorphism group to a subgroup of symmetric group S6. Furthermore, by the properties of 1-regular graph, this paper constructs all the 1-regular Cayley graphs with nonabelian stabilizers and proves that every such graph is not core-free. Thus a classification of such graphs is given.