Doubly chordal graph

Doubly chordal graph --- дважды хордальный граф.

A vertex [math]\displaystyle{ v }[/math] of a graph [math]\displaystyle{ G }[/math] is doubly simplicial if [math]\displaystyle{ v }[/math] is simplicial and has a maximum neighbor. A linear ordering [math]\displaystyle{ (v_{1}, \ldots, v_{n}) }[/math] of the vertices of [math]\displaystyle{ G }[/math] is doubly perfect if for all [math]\displaystyle{ i \in \{1, \ldots, n\} }[/math] [math]\displaystyle{ v_{i} }[/math] is a doubly simplicial vertex of [math]\displaystyle{ G_{i} }[/math] (a subgraph induced by [math]\displaystyle{ v_{i}, \ldots, v_{n} }[/math]). A graph [math]\displaystyle{ G }[/math] is doubly chordal if it admits a doubly perfect ordering. It is known that the powers of a doubly chordal graph are doubly chordal.