Complete multipartite graphs of non-QE class

Nobuaki Obata

Abstract


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.


Keywords


distance matrix, quadratic embedding, quadratic embedding constant (QEC), primary non-QE graph

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DOI: http://dx.doi.org/10.5614/ejgta.2023.11.2.14

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