Wyniki wyszukiwania - BazTech

Ograniczanie wyników

1 Opuscula Mathematica

1 2021

Powiadomienia systemowe

Sesja wygasła!
Sesja wygasła!
Sesja wygasła!
Sesja wygasła!
Sesja wygasła!

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: total connected domination game

Sortuj według:

Ogranicz wyniki do:

Total connected domination game

Bujtas Csilla, Henning Michael A., Irsic Vesna, Klavzar Sandi

Opuscula Mathematica

2021

Vol. 41, no. 4

453--464

The (total) connected domination game on a graph G is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of G. If Dominator starts the game and both players play optimally, then the number of vertices selected during the game is the (total) connected game domination number [formulas] of G. We show that [formulas], and consequently define G as Class i if [formula] for i ∈ {0, 1, 2}. A large family of Class 0 graphs is constructed which contains all connected Cartesian product graphs and connected direct product graphs with minimum degree at least 2. We show that no tree is Class 2 and characterize Class 1 trees. We provide an infinite family of Class 2 bipartite graphs.