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Path polynomials of Trees H n(PDF)

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

Issue:
1997年01期
Page:
77-81
Research Field:
Publishing date:

Info

Title:
Path polynomials of Trees H n
Author(s):
Shi Ronghua
School of Adult Education, NUST, Nanjing 210094
Keywords:
irreducible mat rices characteristic poly nomials connected gr aphs tr ees adjacency mat rix
PACS:
O174
DOI:
-
Abstract:
T he path-polynomial Pk ( λ) , k ≥1, is the characterist ic polynomial of the t ridiagonal mat rix with 1′s on the super and subdiag onals and zeros elsew here; and P0( K) ≡1. T he adjacency mat rix of a connected g raph is any unreduced and symmet rical ( 0, 1) - mat rix . It is of combinat ional signif icance to calculate their path-polynomials. Denote the adjacency mat rix of a graph G by A ( G ) ; if Pn ( A ( G) ) ≥0, for any n, then G is called path-po sit ive gr aph. In this paper, w e completely describe the str ucture formulas of pathpo lynomials of t rees Hn fo r and k≥0 and n≥6; by the w ay, the t ree Hn, n 6, is path-positiv e.

References:

1 Lo vasz L. Combinato rial Pr oblems and Exer cises. Nor thholla nd: Lo ndon, 1979
2 Bapat R B, Lal A K. Path-po sitiv e g r aphs. Linear Algebra and It s Applicatio ns, 1991, 149:125~149
3 Beezer R A. On the polynomial of a path. Linear Alg ebra App1: 1984, 83: 221~225
4 Cv etkov ic D N, Do ob N, Sachs H. Spect ra o f gr aphs. New Yor k: M acm illan Ltd, 1979
5 Big gs N. Algebr aic gr aph theor y. Cambr idge : Cambridg e Univer sity Pr ess, 1974

Memo

Memo:
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Last Update: 2013-03-29