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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 double Roman dominating function (DRDF) on a graph G=(V, E) is a function f: V (G)→{0,
1, 2, 3} having the property that if f (v)= 0, then vertex v has at least two neighbors assigned 2 …

Since 2016, when the first paper of the double Roman domination appeared, the topic has
received considerable attention in the literature. We survey known results on double Roman …

The notion of Roman {2}-domination was introduced in 2016 as a variant of Roman
domination, a concept inspired by a defending strategy used by the emperor Constantine …

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 …

An outer-independent double Italian dominating function (OIDIDF) on a graph $ G $ with
vertex set $ V (G) $ is a function $ f: V (G)\longrightarrow\{0, 1, 2, 3\} $ such that if $ f (v)\in\{0 …

For a graph G=(V, E) with V= V (G) and E= E (G), a Roman {3}-dominating function is a
function f: V→{0, 1, 2, 3} having the property that∑ u∈ NG (v) f (u)≥ 3, if f (v)= 0, and∑ u∈ …

A perfect Italian dominating function on a graph G is a function f: V (G)→{0, 1, 2} satisfying
the condition that for every vertex u with f (u)= 0, the total weight of f assigned to the …

For a graph G=(V, E) G=(V, E), a double Roman dominating function (DRDF) on G is a
function f: V → {0, 1, 2, 3\} f: V→ 0, 1, 2, 3 having the property that if f (v)= 0 f (v)= 0, then …