At its most basic level, this book is about dominating sets in graphs. A dominating set of a
graph G is a subset D of vertices having the property that each vertex of G is in D or is …

In this paper, we continue the study of the domination game in graphs introduced by Brešar
et al.(SIAM J Discret Math 24: 979–991, 2010). We study the total version of the domination …

The recently introduced total domination game is studied. This game is played on a graph G
by two players, named Dominator and Staller. They alternately take turns choosing vertices …

In the domination game on a graph G, the players Dominator and Staller alternately select
vertices of G. Each vertex chosen must strictly increase the number of vertices dominated …

The game total domination number, γ tg, was introduced by Henning et al. in 2015. In this
paper we study the effect of vertex predomination on the game total domination number. We …

In this paper we introduce a domination game based on the notion of connected domination.
Let G=(V, E) be a connected graph of order at least 2. We define a connected domination …

In this paper, we continue the study of the recently introduced total domination game in
graphs. A vertex u in a graph G totally dominates a vertex v if u is adjacent to v in G. A total …

We continue the study of the Grundy domination number of a graph. A linear algorithm to
determine the Grundy domination number of an interval graph is presented. The exact value …

In the domination game, introduced by Bre\v {s} ar, Klav\v {z} ar and Rall in 2010, Dominator
and Staller alternately select a vertex of a graph $ G $. A move is legal if the selected vertex …

In the domination game, two players, the Dominator and Staller, take turns adding vertices of
a fixed graph to a set, at each turn increasing the number of vertices dominated by the set …