Double Roman domination: a survey

D Rupnik Poklukar, J Žerovnik - Mathematics, 2023‏ - mdpi.com
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 …

Triple Roman domination in graphs

HA Ahangar, MP Alvarez, M Chellali… - Applied Mathematics …, 2021‏ - Elsevier
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 …

On the total double Roman domination

Z Shao, J Amjadi, SM Sheikholeslami… - IEEE Access, 2019‏ - ieeexplore.ieee.org
Let G=(V, E) be a simple graph. A double Roman dominating function (DRDF) on G is a
function f from the vertex set V of G into {0, 1, 2, 3} such that if f (u)= 0, then u must have at …

[HTML][HTML] Roman {3}-domination (double Italian domination)

DA Mojdeh, L Volkmann - Discrete Applied Mathematics, 2020‏ - Elsevier
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∈ …

Bounds on the outer-independent double Italian domination number

F Azvin, N Jafari Rad… - … in Combinatorics and …, 2021‏ - comb-opt.azaruniv.ac.ir
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 …

On the outer independent double Roman domination number

DA Mojdeh, B Samadi, Z Shao, IG Yero - Bulletin of the Iranian …, 2022‏ - Springer
An outer independent (double) Roman dominating function is a (double) Roman dominating
function f for which the set of vertices assigned 0 under f is independent. The outer …

Quadruple Roman domination in graphs

J Amjadi, N Khalili - Discrete Mathematics, Algorithms and …, 2022‏ - World Scientific
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 …

Further Progress on the Total Roman -Domination Number of Graphs

H Abdollahzadeh Ahangar, M Chellali, M Hajjari… - Bulletin of the Iranian …, 2022‏ - Springer
For a graph Γ, let γ (Γ), γ t (Γ), and γ t R 2 (Γ) denote the domination number, the total
domination number, and the total Roman {2}-domination number, respectively. It was shown …

Total Roman {3}-domination in graphs

Z Shao, DA Mojdeh, L Volkmann - Symmetry, 2020‏ - mdpi.com
For a graph G=(V, E) with vertex set V= V (G) and edge set E= E (G), a Roman {3}-
dominating function (R {3}-DF) is a function f: V (G)→{0, 1, 2, 3} having the property that∑ …

Covering total double Roman domination in graphs

A Teymourzadeh, DA Mojdeh - … in Combinatorics and …, 2023‏ - comb-opt.azaruniv.ac.ir
For a graph $ G $ with no isolated vertex, a covering total double Roman dominating
function ($ CTDRD $ function) $ f $ of $ G $ is a total double Roman dominating function …