Positive $Q$-matrices of graphs
Studia Mathematica, Tome 179 (2007) no. 1, pp. 81-97
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The $Q$-matrix of a connected graph $\mathcal{G}=(V,E)$ is
$Q=(q^{\partial(x,y)})_{x,y\in V}$,
where $\partial(x,y)$ is the graph distance.
Let $q(\mathcal{G})$ be the range of $q\in(-1,1)$ for which
the $Q$-matrix is strictly positive.
We obtain a sufficient condition for the equality
$q(\widetilde{\mathcal{G}})=q(\mathcal{G})$
where $\widetilde{\mathcal{G}}$ is an extension of
a finite graph $\mathcal{G}$ by joining a square.
Some concrete examples are discussed.
Keywords:
q matrix connected graph mathcal partial where partial graph distance mathcal range which q matrix strictly positive obtain sufficient condition equality widetilde mathcal mathcal where widetilde mathcal extension finite graph mathcal joining square concrete examples discussed
Affiliations des auteurs :
Nobuaki Obata 1
@article{10_4064_sm179_1_7,
author = {Nobuaki Obata},
title = {Positive $Q$-matrices of graphs},
journal = {Studia Mathematica},
pages = {81--97},
publisher = {mathdoc},
volume = {179},
number = {1},
year = {2007},
doi = {10.4064/sm179-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm179-1-7/}
}
Nobuaki Obata. Positive $Q$-matrices of graphs. Studia Mathematica, Tome 179 (2007) no. 1, pp. 81-97. doi: 10.4064/sm179-1-7
Cité par Sources :