Complete multipartite graphs of non-QE class - Nobuaki Obata (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2023)
We derive a formula for the QE constant of a complete multipartite graph and determine the complete multipartite graphs of non-QE class, namely, those which do not admit quadratic embeddings in Euclidean spaces. Moreover, we prove that there are exactly four primary non-QE graphs among the complete multipartite graphs.