# Type of directed graphs

Let $$G=(V,E)$$ be an directed graph such that the following condition holds. If $$(a,b)\in E$$ then there exists $$c\in V\setminus \{a,b\}$$ such that $$(a,c)\in E$$ and $$(c,b)\in E$$.

Question: Was this type of graphs investigated? Does this type of graphs have a name?

• what is "ordered graph"? – Dima Pasechnik Dec 2 '19 at 13:10
• do you mean "directed graph", a.k.a. "digraph" ? – Dima Pasechnik Dec 2 '19 at 13:12
• Yes, i was wrong. – Markiian Khylynskyi Dec 2 '19 at 13:14
• Googling "every edge belongs to a triangle" reveals that this property has been discussed several times, but there is no special term for it. Since your directed version of this property is more special, I expect there is no standard term for it either ... – Nik Weaver Dec 2 '19 at 15:23
• @NikWeaver thanks! – Markiian Khylynskyi Dec 2 '19 at 18:53