Labeling

Labeling --- разметка. A labeling (or valuation) of a graph is any map that carries some set of graph elements to numbers (usually to the positive or non-negative integers). If the domain is the vertex-set, the edge-set, or the set [math]\displaystyle{ V(G) \cup E(G) }[/math], labelings are called respectively vertex-labelings, edge-labelings or total labelings.

Every vertex-labeling induced a natural labeling of the edges: the label of an edge [math]\displaystyle{ uv }[/math] is the absolute value of the difference of the labels of [math]\displaystyle{ u }[/math] and [math]\displaystyle{ v }[/math].