Positive Q-matrices of graphs

Nobuaki Obata. "Positive Q-matrices of graphs." Studia Mathematica 179.1 (2007): 81-97. <http://eudml.org/doc/284747>.

@article{NobuakiObata2007,
abstract = {The Q-matrix of a connected graph = (V,E) is $Q = (q^\{∂(x,y)\})_\{x,y∈ V\}$, where ∂(x,y) is the graph distance. Let q() be the range of q ∈ (-1,1) for which the Q-matrix is strictly positive. We obtain a sufficient condition for the equality q(̃) = q() where ̃ is an extension of a finite graph by joining a square. Some concrete examples are discussed.},
author = {Nobuaki Obata},
journal = {Studia Mathematica},
keywords = {positive definite kernel; Markov sum},
language = {eng},
number = {1},
pages = {81-97},
title = {Positive Q-matrices of graphs},
url = {http://eudml.org/doc/284747},
volume = {179},
year = {2007},
}

TY - JOUR
AU - Nobuaki Obata
TI - Positive Q-matrices of graphs
JO - Studia Mathematica
PY - 2007
VL - 179
IS - 1
SP - 81
EP - 97
AB - The Q-matrix of a connected graph = (V,E) is $Q = (q^{∂(x,y)})_{x,y∈ V}$, where ∂(x,y) is the graph distance. Let q() be the range of q ∈ (-1,1) for which the Q-matrix is strictly positive. We obtain a sufficient condition for the equality q(̃) = q() where ̃ is an extension of a finite graph by joining a square. Some concrete examples are discussed.
LA - eng
KW - positive definite kernel; Markov sum
UR - http://eudml.org/doc/284747
ER -