超立方体三次幂的可区别数研究  

On the distinguishing number of the cube of the hypercube

作　　者：高志军[1] 蔡颖[1] 杜杰[1] 温宇鹏[1] 

机构地区：[1]大连海事大学数学系,辽宁大连116026

出　　处：《大连海事大学学报》2006年第2期121-126,共6页Journal of Dalian Maritime University

摘　　要：根据d维超立方体p次幂结构特性,研究了其顶点间距离与海明距离的关系,给出了确定顶点坐标的充分必要条件,并对d维超立方体三次幂H3d的可区别数进行了研究.得到H3d可区别数的一个上界:D(H3d)≤5(d≥6).This paper studied the relations between the distance and hamming distance between its vertices, and presented the sufficient and necessary conditions for determining the vertex coordinate based on the structural properties of the p powers of the d - dimensional hypercube, and studied the distinguishing number of the cube of the d（≥6） -dimensional hypercube. Finally a correlative conclusion D （Hd^3）≤5 （d≥6） was obtained.

关 键 词：图论 可区别数 超立方体 图着色 

分 类 号：O157.6[理学—数学]