机构地区: 韶关学院
出 处: 《韶关学院学报》 2015年第6期1-4,共4页
摘 要: 设R是一个含有非零单位元的有限交换环,U(R)是R的单位群,G是U(R)的一个乘法子群,S是G的一个非空子集并且S-1={s-1|s∈S}哿S.在研究广义单位Cayley图Γ(R,G,S)的若干性质的基础上,对当S={s}时,Γ(R,U(R),S)的性质作进一步研究,考察Γ(R,U(R),S)的同构问题,得出Γ(R,U(R),S)的团数和顶点着色数,确定Γ(R,U(R),S)是完美图的条件. The paper suggests R be a finite commutative ring with non-zero identity and U(R) be the unit group of R. It also supposes that G is a muhiplicative subgroup of U(R), and S is a non-empty subset of G such that S-1= {s-1|s ∈ S} S. By the structure of a finite commutative ring, have given some properties of a generalization of the unitary Cayley graphs F(R,G,S), where S={s}. The paper makes further research on the properties of F(R, U (R),S) where S={s}, considering the problem of its isomorphism, achieving the clique number and vertex chromatic number of F(R, U(R),S). In addition, it decides F(R, U(R),S) is a key to perfect graphs.