### 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 |
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Pages (from-to) | 81-97 |

Number of pages | 17 |

Journal | Studia Mathematica |

Volume | 179 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 Jul 2 |

Externally published | Yes |

### Keywords

- Graph
- Markov sum
- Positive definite kernel
- Q-matrix

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Obata, N. (2007). Positive Q-matrices of graphs.

*Studia Mathematica*,*179*(1), 81-97. https://doi.org/10.4064/sm179-1-7