Dually vertex-oblique graphs (Q878622)

Let \(G\) be a simple graph on \(n\) vertices. A vertex \(v\) of degree \(dv\) with neighbours of degrees \(x_1\geq x_2\geq\cdots\geq x_{dv}\) has vertex type \(t(v):= (x_1,x_2,\dots, x_{dv})\). \(G\) is vertex-oblique if each vertex has a distinct vertex type. This paper gives a construction of dually center-oblique graphs (the set of vertex types of \(G\) is the same as that of \(\overline G\)).