The distance spectrum of a tree

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.

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Veröffentlicht in:Journal of graph theory 1990-07, Vol.14 (3), p.365-369
1. Verfasser: Merris, Russell
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Sprache:eng
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Combinatorics. Ordered structures
Exact sciences and technology
Mathematics
Sciences and techniques of general use
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container_title Journal of graph theory
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creator Merris, Russell
description 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.
doi_str_mv 10.1002/jgt.3190140309
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subjects Combinatorics. Ordered structures
Exact sciences and technology
Mathematics
Sciences and techniques of general use
title The distance spectrum of a tree
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