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 …

Given real numbers b≥ a> 0, an (a, b)-Roman dominating function of a graph G=(V, E) is a
function f: V→ 0, a, b such that every vertex v with f (v)= 0 has a neighbor u with f (u)= b. An …

The Roman domination in graphs is well-studied in graph theory. The topic is related to a
defensive strategy problem in which the Roman legions are settled in some secure cities of …

Let G=(V, E) be a graph of order n and let B (S) be the set of vertices in V\S that have a
neighbor in the vertex set S. The differential of a vertex set S is defined as∂(S)=| B (S)|—| S …

A Roman $\{2\} $-dominating function (R2F) is a function $ f: V\rightarrow\{0, 1, 2\} $ with the
property that for every vertex $ v\in V $ with $ f (v)= 0$ there is a neighbor $ u $ of $ v $ with …

A maximal double Roman dominating function (MDRDF) on a graph G=(V, E) is a function f:
V (G)→{0, 1, 2, 3} such that (i) every vertex v with f (v)= 0 is adjacent to least two vertices …

Roman domination is an historically inspired variety of domination in graphs, in which
vertices are assigned a value from the set $\{0, 1, 2\} $ in such a way that every vertex …

Roman domination is one of the many variants of domination that keeps most of the
complexity features of the classical domination problem. We prove that Roman domination …

Let G be a finite and simple graph with vertex set V (G). Let f be a function that assigns label
from the set {0, 1, 2, 3, 4, 5} to the vertices of a graph G. For a vertex v∈ V (G), the active …

Abstract A function f: V (G)→{0, 1, 2} is called a Roman dominating function on G=(V (G), E
(G)) if for every vertex v with f (v)= 0, there exists a vertex u∈ NG (v) such that f (u)= 2. A …