Просмотр кода страницы Gamma t(G)-Excellent graph

'''<math>\gamma_{t}(G)</math>-Excellent graph''' ---
<math>\gamma_{t}(G)</math>-превосходный граф. 

A graph <math>G</math> is called '''<math>\gamma_{t}(G)</math>-excellent graph''' if every
vertex of <math>G</math> belongs to some ''total dominating set'' of mini\-mal
cardinality. A family of '''<math>\gamma_{t}(G)</math>-excellent trees''' (trees
where every vertex is in some mini\-mum dominating set) is properly
contained in the set of <math>i</math>-excellent trees (trees where every vertex
is in some  minimum ''independent dominating set'').

In general, for a graph <math>G</math>, let <math>{\mathcal P}</math> denote a property of sets
<math>S \subseteq V</math> of vertices. We call a set <math>S</math> with the property <math>{\mathcal
P}</math> having <math>\{</math> minimum, maximum <math>\}</math>

cardinality <math>\mu(G)</math> a <math>\mu(G)</math>-set. A
vertex is called <math>\mu</math>-good if it is contained in some <math>\mu(G)</math>-set and
<math>\mu</math>-bad otherwise. A graph <math>G</math> is called '''<math>\mu</math>-excellent''' if
every vertex in <math>V</math> is <math>\mu</math>-good.