若干广义圈的Hoffman多项式和谱  

Hoffman Polynomials and Spectra of Some Generalized Cycles

作　　者：邓爱平[1] 王兴斌[2] 李乔[2] 

机构地区：[1]东华大学应用数学系,上海201620 [2]上海交通大学数学系,上海200240

出　　处：《上海交通大学学报》2007年第10期1714-1717,共4页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金资助项目(10301021)

摘　　要：设J和I分别为全1矩阵和单位矩阵.对任一给定正整数k,称邻接矩阵A满足Ak=J(Ak=J-I)的有向图为UPP-k(UPFL-k)有向图.对UPP-k有向图Γ及任意正整数p,确定了Γ是广义圈CpГ的Hoffman多项式和谱;也对UPFL-k有向图给出了广义圈CpГ的Hoffman多项式及CkГ的谱的明确表达式.Let J and I be the matrix of all ones and the identity matrix,respectively. For any fixed positive integer k, a digraph F is called a UPP-k（UPFL-k, resp. ）digraph if its adjacency matrix A satisfies A^k =J（A^k =J-I,resp. ）. Given a positive integer p and a UPP-k digraph Г, the Hoffman polynomial and the spectrum of the generalized cycle Cp×Г are obtained. For a UPFL-k digraph Г, explicit expressions for the Hoffman polynomial of Cp×P and the spectrum of Ck×Г are also provided.

关 键 词：广义圈 Hoffman多项式 谱 

分 类 号：O157.5[理学—数学]