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 …

Abstract The Maker–Breaker total domination game in graphs is introduced as a natural
counterpart to the Maker–Breaker domination game recently studied by Duchêne, Gledel …

Abstract We introduce the Maker–Breaker domination game, a two player game on a graph.
At his turn, the first player, Dominator, selects a vertex in order to dominate the graph while …

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 …

Domination game is a game on a simple graph played by two players, Dominator and Staller
who are alternating in taking turns. In each turn a player chooses a vertex in such a way that …

A vertex in a graph totally dominates another vertex if they are adjacent. A sequence of
vertices in a graph G is called a total dominating sequence if every vertex v in the sequence …

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 …

Graph theory is an important area of Applied Mathematics with a broad spectrum of
applications in many fields. In the Call for Papers for this issue, I asked for submissions …