A finite simple connected graph 
is quadratically embeddable if its quadratic
embedding constant 
is nonpositive, i.e., 
.
A graph being quadratically embeddable is equivalent to its graph distance matrix being conditionally negative definite (Obata and Zakiyyah 2018,
Obata 2022, Choudhury and Nandi 2023), i.e., it satisfying 
for all 
such that 
(Dyn et al. 1986).
numbers of quadratically embeddable graphs on 
, 2, ... vertices are 1, 1, 2, 6, 19, 85, 452, 3174, 26898,
... (OEIS A363960). The corresponding numbers
of non-quadratically embeddable graph are 0, 0, 0, 0, 2, 27, 401, 7943, 234182, ...
(OEIS A363961). All connected graphs on 
nodes are therefore quadratically embeddable, and the smallest non-quadratically
embeddable graphs are the two graphs on 5 vertices consisting of the complete
bipartite graph 
and the graph obtained from the wheel
graph 
by removing one spoke (Obata and Zakiyyah 2018).
Trees are quadratically embeddable (Obata and Zakiyyah 2018).
The quadratic embedding constant of a graph Cartesian product of graphs 
,
,
... each having two or more vertices has 
, making them quadratically
embeddable (Obata 2022).
