On quadratic embedding constants of star product graphs

Wojciech Mlotkowski, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

A connected graph G is of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently if the distance matrix is conditionally negative definite, or equivalently if the quadratic embedding constant QEC(G) is non-positive. For a finite star product of (finite or infinite) graphs G = G1 *...* Gr an estimate of QEC(G) is obtained after a detailed analysis of the minimal solution of a certain algebraic equation. For the path graph Pn an implicit formula for QEC(Pn) is derived, and by limit argument QEC(Z) = QEC(Z+) =-1=2 is shown. During the discussion a new integer sequence is found.

Original languageEnglish
Pages (from-to)129-163
Number of pages35
JournalHokkaido Mathematical Journal
Volume49
Issue number1
DOIs
Publication statusPublished - 2020

Keywords

  • Conditionally negative definite matrix
  • Distance matrix
  • QE constant
  • Quadratic embedding
  • Star product graph

ASJC Scopus subject areas

  • Mathematics(all)

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