Labeling of type (a,b,c)

Labeling of type [math]\displaystyle{ (a,b,c) }[/math] --- разметка типа [math]\displaystyle{ (a,b,c) }[/math].

A labeling of type [math]\displaystyle{ (a,b,c) }[/math] assigns labels from the set

[math]\displaystyle{ \{1,2,3,\ldots, a|V(G)|+ b|E(G)| + c|F(G)|\} }[/math]

to the vertices, edges and faces of [math]\displaystyle{ G }[/math] such that each vertex receives [math]\displaystyle{ a }[/math] labels, each edge receives [math]\displaystyle{ b }[/math] labels and each face receives [math]\displaystyle{ c }[/math] labels and each number is used exactly once as a label. Labelings of type [math]\displaystyle{ (1,0,0) }[/math], [math]\displaystyle{ (0,1,0) }[/math] and [math]\displaystyle{ (0,0,1) }[/math] are also called vertex, edge and face labelings, respectively.