Distance matrices and quadratic embedding of graphs

Nobuaki Obata, Alfi Y. Zakiyyah

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)37-60
ページ数24
ジャーナルElectronic Journal of Graph Theory and Applications
6
1
DOI
出版ステータスPublished - 2018

ASJC Scopus subject areas

  • 離散数学と組合せ数学
  • 応用数学

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