Triangular vertex

Triangular vertex --- триангулированная вершина. A vertex [math]\displaystyle{ u }[/math] is a triangular vertex, if every vertex in the open neighborhood [math]\displaystyle{ N(u) }[/math] is in a triangle with [math]\displaystyle{ u }[/math]. Stated equivalently, a vertex is triangular, if the induced subgraph [math]\displaystyle{ [G(N(u)] }[/math] contains no isolated vertices. Notice if a vertex [math]\displaystyle{ u }[/math] is triangular, then [math]\displaystyle{ deg(u) \geq 2 }[/math]. We say that a graph [math]\displaystyle{ G }[/math] is triangular, if it contains at least one triangular vertex, and is completely triangular, if every vertex in [math]\displaystyle{ G }[/math] is triangular.