Originally Posted by

**HappyJoe** In graph theory, labels can be assigned to either vertices or edges (or both), and I guess that your article attempts to cover both cases.

As for the restriction question, you can consider L as a function from V U E into some set of labels, i.e. L takes either a vertex or an edge and gives it some label. The set V' U E' is just a subset of V U E, and so you define L' to be the restriction of L (as a function) to the set V' U E'. Do you know what the restriction of a function means?

As for the union of V' and E', where V' = {1,2,3,4} and E' = {(1,2), (1,3), (2,3), (2,4) }, it is just that:

V' U E' = {1,2,3,4, (1,2), (1,3), (2,3), (2,4)},

so V' U E' is a set, in which elements are either vertices or edges (they have been mixed, so to speak).