On Tetha-graphs of partial cubes
Sandi Klavžar, Matjaž Kovše · Discussiones Mathematicae Graph Theory · 2007
The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation.Θ-graphs that are 2-connected, trees, or complete graphs are characterized.In particular, Θ(G) is complete if and only if G can be obtained from K 1 by a sequence of (newly introduced) dense expansions.Θ-graphs are also compared with familiar concepts of crossing graphs and τ -graphs.