Edge-graceful labeling

Edge-graceful labeling --- рёберно-грациозная разметка.

Edge-graceful labeling of graphs was introduced by Lo in 1985. Let [math]\displaystyle{ G(V,E) }[/math] be a simple graph with [math]\displaystyle{ |V| = p }[/math] and [math]\displaystyle{ |E| = q }[/math]. Then, [math]\displaystyle{ G }[/math] is said to be edge-graceful if there exits a bijection [math]\displaystyle{ f: \; E \rightarrow \{1, 2, \ldots, q\} }[/math] such that the induced mapping [math]\displaystyle{ f^{+}: \; V \rightarrow \{0, 1, 2, \ldots, p-1\} }[/math], defined by

[math]\displaystyle{ f^{+}(v) = \sum_{uv \in E}f(uv)\pmod{p} }[/math]

is also a bijection.