5阶图的结构完全正

1 简 介称n阶双非负矩阵,即非负半正定矩阵A为完全正的,如果A可分解为BBt,其中B是n×m的非负矩阵.或等价地,有n维非负向量β1,β2,…,βm使得A=β1β1t+…+βmβmt,B的可能最小的列数m称为A的分解指数（或A的CP秩）,记作 ψ（A）（或CPrankA）.记DPn为所有n阶双非负矩阵构成的集合;CPn为所有n阶完全正矩阵构成的集合.判断一个双非负矩阵是否为完全正以及确定它的分解指数是完全正矩阵研究的两个基本问题.对完全正矩阵的研究始于本世纪六十年代初,它的应用非常广泛,涉及组合设计

STRUCTURAL COMPLETELY POSITIVE GRAPHS OF ORDER 5

An n ×n entrywise nonnegative matrix A is called doubly nonnegativeif A is also semidefinite positive as well. A graph G is called structural cp if all ofits doubly nonnegative structural matrices are completely positive, where a struc-tural matrix A= (aij) of G is defined as aij＝1, if (i,j) ∈E(G) and 0, if (i,j) E(G) for all i≠j. This paper fully characterizes the structural cp matrices of order5.