Type: Article
Publication Date: 2018-04-03
Citations: 15
DOI: https://doi.org/10.5614/ejgta.2018.6.1.4
A connected graph is said to be of Q E 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 Q E class are derived from the point of view of graph operations. For a quantitative criterion the Q E constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the Q E constant coincides with the second largest eigenvalue of the distance matrix. The Q E constants are determined for all graphs on n vertices with n ≤ 5 , among which two are not of Q E class.