Просмотр кода страницы Total dominating function

'''Total dominating function''' --- тотально доминирующая функция. 

As a fractional generalization of the '' total dominating set'', a
''' total dominating function''' (TDF) of a graph <math>G = (V,E)</math> is
defined as a function <math>f: V \rightarrow [0,1]</math> such that <math>\sum_{u \in
N(v)} f(u) \geq 1</math> for each <math>v \in V</math>. (Here <math>N(v)</math> is the open
neighborhood of <math>v</math>.) A TDF <math>f</math> is minimal (MTDF) if no function <math>g: V
\rightarrow [0,1]</math> with <math>g < f</math> is also a TDF of <math>G</math>, where <math>g < f</math>
means that <math>g(v) \leq f(v)</math> for each <math>v \in V</math> and <math>f \neq g</math>.
Obviously, an integer-valued (minimal) TDF is exactly the
characteristic function of a (minimal) '' total dominating set''.