Distance matrices and quadratic embedding of graphs

Nobuaki Obata, Alfi Y. Zakiyyah

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on n vertices with n ≤ 5, among which two are not of QE class.

Original languageEnglish
Pages (from-to)37-60
Number of pages24
JournalElectronic Journal of Graph Theory and Applications
Volume6
Issue number1
DOIs
Publication statusPublished - 2018 Jan 1

Keywords

  • Conditionally negative definite matrix
  • Distance matrix
  • Euclidean distance matrix quadratic embedding
  • QE constant

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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