CAJ | 학술논문

设G是一个有限群，在G上定义一类新的共轭类图ΓG ：以G的所有共轭类构成的集合为顶点集，两个不同的共轭类之间用一条边相连当且仅当这两个共轭类的长度互素．通过定义的共轭类图得到了一些图性质且通过图性质刻画了一些群的结构，如ΓG 碖 K 3当且仅当G 碖 Z3或S 3．特别地，获得了二面体群共轭类图的一些性质．最后，应用共轭类图的性质得到了一些群的性质．
설G시일개유한군，재G상정의일류신적공액류도ΓG ：이G적소유공액류구성적집합위정점집，량개불동적공액류지간용일조변상련당차부당저량개공액류적장도호소．통과정의적공액류도득도료일사도성질차통과도성질각화료일사군적결구，여ΓG 론 K 3당차부당G 론 Z3혹S 3．특별지，획득료이면체군공액류도적일사성질．최후，응용공액류도적성질득도료일사군적성질．
A new graph ΓG of conjugacy classes of a finite group G is defined :its verticesare the conjugacy classes of G and two distinct vertices join by an edge if their sizes are coprime .By the defini-tion of ΓG ,we obtain some graph theoretical properties of ΓG and characterize some structures of fi-nite groups by their conjugate graphs .For example ,ΓG ≌ K3 if and only if G≌ Z3 or S3 .In particu-lar ,we prove some properties of the conjugate graphs of dihedral groups .Finally ,we obtain some properties of finite groups by applying properties of the conjugate graphs of finite groups .