[1]施容华,郑寿炳.某些矩阵的道路多项式[J].南京理工大学学报(自然科学版),1996,(02):82-86.
　Shi Ronghua Zheng Shoubing.The Path polynomials Evaluated at Some Matrices[J].Journal of Nanjing University of Science and Technology,1996,(02):82-86.
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某些矩阵的道路多项式()
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《南京理工大学学报》（自然科学版）[ISSN:1005-9830/CN:32-1397/N]

卷:
期数:
1996年02期
页码:
82-86
栏目:
出版日期:
1996-04-30

文章信息/Info

Title:
The Path polynomials Evaluated at Some Matrices
作者:
施容华; 郑寿炳
( 南京理工大学成人教育学院, 南京210094) 　( 南京市教育学院数学系, 南京210008)
Author(s):
Shi Ronghua Zheng Shoubing ①
School of Adult Education, NUST, Nanjing 210094)
关键词:
矩阵( 数学) ;  特征多项式;  连通图;  树( 数学)
Keywords:
mat rix es ( mathemat ics ) ;  characterist ic polynomial;  connected graph;  t rees ( mathemat ics)
分类号:
O151.21
摘要:
Ｐｋ（λ）表示上、下对角线元素为１，其余位置元素是０的ｋ阶方阵的特征多项式，ｋ≥１。如果Ｐｋ（Ａ）≥０，ｋ＝１，２，…，Ａ是ｎ阶方阵，则说Ａ是道路正矩阵。当图的邻接矩阵是道路正矩阵时，称这个图是道路正图。该文对任何ｋ≥０，分别给出了图Ｄ、Ｅ、Ｆ的邻接矩阵的道路多项式的表达式。这些工作是进一步研究不可约（０，１）对称矩阵的道路多项式的基础。
Abstract:
For any po sit ive integer k ≥ 1, the paper denoted by Pk ( K) the char acteristic polynomial of the t ridiag onal matr ix w ith 1ps on the super -and subdiago nals and zeres elsew here. The n×n square mat rix A is said to be path-posit iv e if Pk ( A ) ≥ 0 for k= 1, 2, 3, ? A graph is said to path-po sit iv e if and only if the adjacency matrix of the g raph is path-posit ive. This paper has derived the str ucture formulas of path-po lynomials evaluated at the adjacency matr ices of gr aphs D , E and F , respect iv ely . T his w ork serves as the basis for further invest ig at ing the behavior of P k( A ) ev aluated at arbit rary unreduced ( 0, 1) symmet ric mat rices.

参考文献/References:

1　Beezer R A. On the polynomial of a path. Linear Alg ebra Appl, 1984, 63: 221～225
2　Cv etkov ic D M, Doo b M, Sachs H. Spect ra o f gr aphs. New Yor k: Academ ic, 1979
3　Lo vasz La slo . Combinato rial pr oblems and ex ercises, New Yo rk : Nor th Ho lland, 1979
4　Bapat R B, I al A K. Path-positiv e g ra phs. Linear Algebr a and I ts Applicdtio ns, 1991, 149:125～149
5　Big gs N. Algebr aic gr aph theor y. Cambr idge : Cambridg e Univer sity Pr ess, 1974

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备注/Memo

备注/Memo:
国家自然科学基金资助课题
施容华　男　50 岁　教授
更新日期/Last Update: 2013-04-11