The distance spectrum of a tree

Let T be a tree with line graph T*. Define K = 2I + A(T*), where A denotes the adjacency matrix. Then the eigenvalues of ‐2K−1 interlace the eigenvalues of the distance matrix D. This permits numerous results about the spectrum of K to be transcribed for the less tractable D.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of graph theory 1990-07, Vol.14 (3), p.365-369
1. Verfasser:	Merris, Russell
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics. Ordered structures Exact sciences and technology Mathematics Sciences and techniques of general use
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	Let T be a tree with line graph T. Define K = 2I + A(T), where A denotes the adjacency matrix. Then the eigenvalues of ‐2K−1 interlace the eigenvalues of the distance matrix D. This permits numerous results about the spectrum of K to be transcribed for the less tractable D.
ISSN:	0364-9024 1097-0118
DOI:	10.1002/jgt.3190140309