Name and notation for all arcs from outside a subset S to any node in S in a graph

Question

I have a directed graph G with nodes:

1,2,3

And arcs: (i,j): from i to j

(1,2)
(2,1)
(2,3)
(3,4)

Which gives:

1 <-> 2 -> 3 -> 4 

Is there a word and notation for all arcs entering a subset. So if my subset would be nodes {2,3}, the subset would consists of arc (1,2)?

Answer 1

This is often notated $\delta_G^-(S)$ (or $\delta^-(S)$ if the graph is clear) and can simply be called, as you said, the set of arcs entering $S$. For instance, see the Preliminaries sections in these papers.