Positive Q-matrices of graphs

Nobuaki Obata

doi:10.4064/sm179-1-7

Positive Q-matrices of graphs

Nobuaki Obata

Center for Data-driven Science and Artificial Intelligence (CDS)

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

The Q-matrix of a connected graph G = (V,E) is Q = (q ^∂(x,y))x,yεv, where ∂(x,y) is the graph distance. Let q(G] be the range of q ε (-1,1) for which the Q-matrix is strictly positive. We obtain a sufficient condition for the equality q(G̃) = q(G) where g̃ is an extension of a finite graph G by joining a square. Some concrete examples are discussed.

Original language	English
Pages (from-to)	81-97
Number of pages	17
Journal	Studia Mathematica
Volume	179
Issue number	1
DOIs	https://doi.org/10.4064/sm179-1-7
Publication status	Published - 2007

Keywords

Graph
Markov sum
Positive definite kernel
Q-matrix

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10.4064/sm179-1-7

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AB - The Q-matrix of a connected graph G = (V,E) is Q = (q ∂(x,y))x,yεv, where ∂(x,y) is the graph distance. Let q(G] be the range of q ε (-1,1) for which the Q-matrix is strictly positive. We obtain a sufficient condition for the equality q(G̃) = q(G) where g̃ is an extension of a finite graph G by joining a square. Some concrete examples are discussed.

KW - Graph

KW - Markov sum

KW - Positive definite kernel

KW - Q-matrix

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JO - Studia Mathematica

JF - Studia Mathematica

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Positive Q-matrices of graphs

Abstract

Keywords

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