While concepts related to domination in graphs can be traced back to the Roman Empire in
the fourth century AD and to the mid-1800s in connection with various chessboard problems …

This chapter is concerned with the concept Roman domination in graphs, which was
introduced in 2004 by Cockayne, Dreyer, SM Hedetniemi, and ST Hedetniemi based on the …

A Roman dominating function on a graph G is a function f: V (G)→{0, 1, 2} satisfying the
condition that every vertex u for which f (u)= 0 is adjacent to at least one vertex v for which f …

In this paper we present a brief survey of bounds on selected domination parameters. We
focus primarily on bounds on domination parameters in terms of the order and minimum …

The purpose of this survey is to bring some order into the growing literature on a type of
graphs which emerged in the past couple of decades under a wealth of names and in …

We define a total coalition in a graph G as a pair of disjoint subsets A 1, A 2⊆ A that satisfy
the following conditions:(a) neither A 1 nor A 2 constitutes a total dominating set of G, and (b) …

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 …

Let $ G $ be a simple graph with vertex set $ V $. A double Roman dominating function
(DRDF) on $ G $ is a function $ f: V\rightarrow\{0, 1, 2, 3\} $ satisfying that if $ f (v)= 0$, then …