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The Path polynomials Evaluated at Some Matrices(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1996年02期
Page:
82-86
Research Field:
Publishing date:

Info

Title:
The Path polynomials Evaluated at Some Matrices
Author(s):
Shi Ronghua Zheng Shoubing ①
School of Adult Education, NUST, Nanjing 210094)
Keywords:
mat rix es ( mathemat ics ) characterist ic polynomial connected graph t rees ( mathemat ics)
PACS:
O151.21
DOI:
-
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.

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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Memo:
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Last Update: 2013-04-11