On graphs with small game domination number

Sandi Klavzar (1) , Gasper Kosmrlj (2) , Simon Schmidt (3)

1 FMF - Faculty of Mathematics and Physics [Ljubljana]
2 Departement of Mathematics [Slovenia]
3 IF - Institut Fourier

The domination game is played on a graph G by Dominator and Staller. The game domination number γg(G) of G is the number of moves played when Dominator starts and both players play optimally. Similarly, γ′g(G) is the number of moves played when Staller starts. Graphs G with γg(G)=2, graphs with γ′g(G)=2, as well as graphs extremal with respect to the diameter among these graphs are characterized. In particular, γ′g(G)=2 and diam(G)=3 hold for a graph G if and only if G is a so-called gamburger. Graphs G with γg(G)=3 and diam(G)=6, as well as graphs G with γ′g(G)=3 and diam(G)=5 are also characterized

Domaines: Mathématiques [math]

Sandi Klavzar, Gasper Kosmrlj, Simon Schmidt. On graphs with small game domination number. Applicable Analysis and Discrete Mathematics, 2016, 10 (1), pp.30-45. ⟨10.2298/AADM160207003K⟩. ⟨hal-01992740⟩