Complete Multipartite Graphs of Non-QE Class
Nobuaki Obata
TL;DR
This paper derives a formula for the QE constant of complete multipartite graphs and characterizes those that cannot be embedded quadratically in Euclidean space, identifying primary non-QE graphs.
Contribution
It provides a formula for the QE constant and classifies complete multipartite graphs based on their quadratic embeddability in Euclidean space.
Findings
Derived a formula for the QE constant of complete multipartite graphs
Identified complete multipartite graphs that are non-QE class
Specified primary non-QE graphs among these graphs
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 a Euclidean space. Moreover, the primary non-QE graphs are specified among the complete multipartite graphs.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · graph theory and CDMA systems