Vertex-antimagic total labeling

Vertex-antimagic total labeling --- вершинно-антимагическая тотальная разметка.

A bijection [math]\displaystyle{ \lambda: \; V \cup E \rightarrow \{1,2, \ldots, ||V| + |E|\} }[/math] is called a vertex-antimagic total labeling of [math]\displaystyle{ G = (V,E) }[/math], if the weights of vertices [math]\displaystyle{ wt(x) }[/math], [math]\displaystyle{ x \in V }[/math], are distinct. A bijection [math]\displaystyle{ \lambda: \; V \cup E \rightarrow \{1,2, \ldots, ||V| + |E|\} }[/math] is called an [math]\displaystyle{ (a,d) }[/math]-vertex-antimagic total labeling of [math]\displaystyle{ G = (V,E) }[/math] if the set of vertex weights [math]\displaystyle{ W = \{wt(x)| \; x \in V\} = \{a, a+d, \ldots, a+(|V|-1)d\} }[/math] for some integers [math]\displaystyle{ a }[/math] and [math]\displaystyle{ d }[/math].

See also

• Magic labeling.