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Mean distance in a tree

โœ Scribed by Peter Winkler

Book ID
104184111
Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
348 KB
Volume
27
Category
Article
ISSN
0166-218X

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## 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 โ€2__K__^โˆ’1^ interlace the eigenvalues of the distance matrix __D__. This permits numerous results about the spectrum of __K__ to be tran

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## Abstract We investigate distance vectors in trees and introduce a new center concept based on the notion of majorization and discuss relations to location theory. For a tree __T__ and a vertex __v__ โˆˆ __T__, we define the distance vector __d__(__v__,ยท) = (__d__(__v__,__w__) __w__ โˆˆ __T__), where