The Q-matrix of a connected graph = (V,E) is , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-7,
author = {Nobuaki Obata},
title = {Positive Q-matrices of graphs},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {81-97},
zbl = {1112.05068},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-7}
}
Nobuaki Obata. Positive Q-matrices of graphs. Studia Mathematica, Tome 178 (2007) pp. 81-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-1-7/