Positive Q-matrices of graphs

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6 Citations (Scopus)


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 languageEnglish
Pages (from-to)81-97
Number of pages17
JournalStudia Mathematica
Issue number1
Publication statusPublished - 2007


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


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