Constructions for type I trees with nonisomorphic Perron branches

Stephen J. Kirkland

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 3, page 617-632
  • ISSN: 0011-4642

Abstract

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A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between characteristic vertices, algebraic connectivity, and Perron values of certain positive matrices associated with the tree.

How to cite

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Kirkland, Stephen J.. "Constructions for type I trees with nonisomorphic Perron branches." Czechoslovak Mathematical Journal 49.3 (1999): 617-632. <http://eudml.org/doc/30510>.

@article{Kirkland1999,
abstract = {A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between characteristic vertices, algebraic connectivity, and Perron values of certain positive matrices associated with the tree.},
author = {Kirkland, Stephen J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {weighted graph; Laplacian matrix; algebraic connectivity},
language = {eng},
number = {3},
pages = {617-632},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Constructions for type I trees with nonisomorphic Perron branches},
url = {http://eudml.org/doc/30510},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Kirkland, Stephen J.
TI - Constructions for type I trees with nonisomorphic Perron branches
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 3
SP - 617
EP - 632
AB - A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between characteristic vertices, algebraic connectivity, and Perron values of certain positive matrices associated with the tree.
LA - eng
KW - weighted graph; Laplacian matrix; algebraic connectivity
UR - http://eudml.org/doc/30510
ER -

References

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