...and for other kinds of digraphs where the notion makes sense, such as maybe join/meet semilattice digraphs, and possibly even partial order digraphs in general.
And correspondingly, there could be an attribute JoinIrreducibleVertices, etc.
This is just an idea!
There's a very slight possibility that this could ultimately be used by the Semigroups package, where there exist functions such as IsJoinIrreducible and JoinIrreducibleDClasses.
The notion of join/meet primality might also be good to have https://en.wikipedia.org/wiki/Lattice_(order)#Important_lattice-theoretic_notions
...and for other kinds of digraphs where the notion makes sense, such as maybe join/meet semilattice digraphs, and possibly even partial order digraphs in general.
And correspondingly, there could be an attribute
JoinIrreducibleVertices, etc.This is just an idea!
There's a very slight possibility that this could ultimately be used by the Semigroups package, where there exist functions such as
IsJoinIrreducibleandJoinIrreducibleDClasses.The notion of join/meet primality might also be good to have https://en.wikipedia.org/wiki/Lattice_(order)#Important_lattice-theoretic_notions