✦ LIBER ✦

The distance spectrum of a tree

✍ Scribed by Russell Merris

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 240 KB
Volume: 14
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190140309

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let T be a tree with line graph T*. Define K = 2__I__ + A(T*), where A denotes the adjacency matrix. Then the eigenvalues of ‐2__K__^−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.

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