Objects, Invariants and Properties for Graph Theory (GT) automated conjecturing: in particular with the Sage program CONJECTURING: http://nvcleemp.github.io/conjecturing/
Graph('HnLk]My') #Nce to ((diameter_equals_two)&(is_overfull))->(is_maximal_triangle_free)
Graph('G@GQSK') #Nce to ((matching_covered)^(is_not_forest))->(is_maximal_triangle_free)
Graph('OzK[]L@gA`DEDEAj?msCu') #Nce to ((~(order_leq_twice_max_degree))&(diameter_equals_two))->(is_maximal_triangle_free)