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The distance spectrum of a tree
Author(s) -
Merris Russell
Publication year - 1990
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190140309
Subject(s) - mathematics , combinatorics , adjacency matrix , distance matrix , eigenvalues and eigenvectors , spectrum (functional analysis) , tree (set theory) , graph , distance matrices in phylogeny , adjacency list , matrix (chemical analysis) , spectrum of a matrix , line (geometry) , discrete mathematics , matrix differential equation , geometry , mathematical analysis , physics , materials science , quantum mechanics , composite material , differential equation
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 .