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Roman and Double Roman Domination Numbers for Wheel, Ladder, and Fan Graphs

International Journal of Mathematics Trends and Technology
We determine exact values of the Roman domination number γR(G) and the double Roman domination number γdR(G) for three foundational families of graphs: wheel graphs Wn (n ≥ 3), ladder graphs Ln (n ≥ 2), and fan graphs Fn (n ≥ 2).
Athraa T. Breesam
semanticscholar   +2 more sources

Bounds on signed total double Roman domination [PDF]

Communications in Combinatorics and Optimization, 2020
A signed total double Roman dominating function (STDRDF) on {an} isolated-free graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{-1,1,2,3\}$ such that (i) every vertex $v$ with $f(v)=-1$ has at least two neighbors assigned 2 under $f$ or one neighbor ...
L. Shahbazi, H. Abdollahzadeh Ahangar, R. Khoeilar, S.M. Sheikholeslami   +3 more
doaj   +1 more source

Calculating Modern Roman Domination of Fan Graph and Double Fan Graph [PDF]

Journal of Applied Sciences and Nanotechnology, 2022
This paper is concerned with the concept of modern Roman domination in graphs. A Modern Roman dominating function on a graph is labeling such that every vertex with label 0 is adjacent to two vertices; one of them of label 2 and the other of label 3 and ...
Saba Salah, Ahmed Omran, Manal Al-Harere
doaj   +1 more source

Bounds on the global double Roman domination number in graphs [PDF]

Discussiones Mathematicae Graph Theory, 2022
Let $G$ be a simple graph of order $n$ and let $\gamma_{gdR}(G)$ be the global double Roman domination number of $G$. In this paper, we give some upper bounds on the global double Roman domination number of $G$.
Guoliang Hao, Shouliu Wei, Seyed Mahmoud Sheikholeslami, Xiaodan Chen   +3 more
doaj   +2 more sources

On the D-differential of a graph

AKCE International Journal of Graphs and Combinatorics, 2022
Let [Formula: see text] be a graph of order n(G). For a subset S of V(G), the boundary of S is defined as [Formula: see text] where N(S) is the open neighborhood of S.
Kijung Kim
doaj   +1 more source

Double Roman reinforcement number in graphs

AKCE International Journal of Graphs and Combinatorics, 2021
For a graph a double Roman dominating function is a function having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one ...
J. Amjadi, H. Sadeghi
doaj   +1 more source

Double Roman Graphs in P(3k, k)

Mathematics, 2021
A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} with the properties that if f(u)=0, then vertex u is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and if f(u)=1, then vertex u is ...
Zehui Shao, Rija Erveš, Huiqin Jiang, Aljoša Peperko, Pu Wu, Janez Žerovnik   +5 more
doaj   +1 more source

Bounds on the total double Roman domination number of graphs [PDF]

, 2023
Let $G$ be a simple graph with no isolated vertex and let $\gamma_{tdR}(G)$ be the total double Roman domination number of $G$. In this paper, we present lower and upper bounds on $\gamma_{tdR}(G)$ of a graph $G$ in terms of the order, open packing ...
Xie, Zhihong, Hajjari, Maryam, Zhihong Xie, Seyed Mahmoud Sheikholeslami, Sheikholeslami, Seyed Mahmoud, M. Hajjari, Guoliang Hao, Hao, Guoliang   +7 more
core   +1 more source

Further results on independent double roman trees

AKCE International Journal of Graphs and Combinatorics, 2022
A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v
A. Rahmouni, H. Abdollahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami   +3 more
doaj   +1 more source

An improved upper bound on the independent double Roman domination number of trees

AKCE International Journal of Graphs and Combinatorics, 2022
For a graph [Formula: see text] an independent double Roman dominating function (IDRDF) is a function [Formula: see text] having the property that: (i) every vertex [Formula: see text] with f(v) = 0 has a neighbor u with f(u) = 3 or at least two ...
F. Nahani Pour, H. Abdollahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami   +3 more
doaj   +1 more source