Primary Non-QE Graphs on Six Vertices

Abstract

A connected graph is called of non-QE class if it does not admit a quadratic embedding in a Euclidean space. A non-QE graph is called primary if it does not contain a non-QE graph as an isometrically embedded proper subgraph. The graphs on six vertices are completely classified into the classes of QE graphs, of non-QE graphs, and of primary non-QE graphs.