Pseudograceful graph

Pseudograceful graph --- псевдограциозный граф.

A graph [math]\displaystyle{ G = (V,E) }[/math] such that [math]\displaystyle{ |V| \leq |E| + 1 }[/math] is said to be pseudograceful, if there exists an injective function called pseudograceful labelling [math]\displaystyle{ f: \, V \rightarrow \{0, 1, \ldots, |E| - 1, |E| + 1\} }[/math] such that the induced function

[math]\displaystyle{ f^{\ast}: \, E(G) \rightarrow \{1, 2, \ldots, |E(G)|\} }[/math]

defined by

[math]\displaystyle{ f^{\ast}(xy) = |f(x) - f(y)|\mbox{ for all } xy \in E(G) }[/math]

is an injection.

See also

• Graceful graph.