FACTORING DISTANCE MATRIX POLYNOMIALS

Authors
COLLINS KL
Citation
Kl. Collins, FACTORING DISTANCE MATRIX POLYNOMIALS, Discrete mathematics, 122(1-3), 1993, pp. 103-112
Citations number
15
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Discrete mathematics → ACNP
ISSN journal
0012365X
Volume
122
Issue
1-3
Year of publication
1993
Pages
103 - 112
Database
ISI
SICI code
0012-365X(1993)122:1-3<103:FDMP>2.0.ZU;2-Q
Abstract
In this paper we prove that a vertex-centered automorphism of a tree g ives a proper factor of the characteristic polynomial of its distance or adjacency matrix. We also show that the characteristic polynomial o f the distance matrix of any graph always has a factor of degree equal to the number of vertex orbits of the graph. These results are applie d to full k-ary trees and some other problems.