@article{10.5614/ejgta.2018.6.1.4,
author = {Nobuaki Obata and Alfi Y. Zakiyyah},
title = {Distance Matrices and Quadratic Embedding of Graphs},
number = {1},
volume = {6},
journal = {Electronic Journal of Graph Theory and Applications},
year = {2018},
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 $n\le5$, among which two are not of QE class.},
doi = {10.5614/ejgta.2018.6.1.4},
pages = {37--60},
}