Results 31 to 40 of about 5,939,930 (166)

Minimal Roman Dominating Function

International Journal of Mathematics and Soft Computing, 2017
In this paper, the concept of Minimal Roman Dominating Function is considered. A characterization of a Minimal Roman Dominating Function has been given. It has also been proved that for any graph with vertices, the Upper Roman Domination Number is . It is also shown that if is a Minimal Roman Dominating Function then is a Roman Dominating Function for ...
Sanket Mukundbhai Badiyani, D. K. Thakkar   +1 more
openaire   +1 more source

A note on the edge Roman domination in trees

Electronic Journal of Graph Theory and Applications, 2017
A subset $X$ of edges of a graph $G$ is called an \textit{edgedominating set} of $G$ if every edge not in $X$ is adjacent tosome edge in $X$. The edge domination number $\gamma'(G)$ of $G$ is the minimum cardinality taken over all edge dominating sets of 
Nader Jafari Rad
doaj   +1 more source

Bounds on the Double Italian Domination Number of a Graph

Discussiones Mathematicae Graph Theory, 2022
For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
doaj   +1 more source

On the Roman Edge Domination Number of a Graph [PDF]

, 2010
Let G be a simple graph with vertex set V (G) and edge set E(G)
K. Ebadi, Ebadi, K., Khodadadi, E., E. Khodadadi, L. Pushpalatha, Pushpalatha, L.   +5 more
core   +1 more source

Some Properties of Double Roman Domination

Discrete Dynamics in Nature and Society, 2020
A double Roman dominating function on a graph G is a function f:VG⟶0,1,2,3 satisfying the conditions that every vertex u for which fu=0 is adjacent to at least one vertex v for which fv=3 or two vertices v1 and v2 for which fv1=fv2=2 and every vertex u ...
Hong Yang, Xiaoqing Zhou
doaj   +1 more source

Double Roman domination and domatic numbers of graphs

Communications in Combinatorics and Optimization, 2018
A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in \cite{bhh} as a function‎ ‎$f:V(G)\rightarrow\{0,1,2,3\}$ having the property that if $f(v)=0$‎, ‎then the vertex $v$ must have at least two‎ ‎neighbors assigned 2 ...
L. Volkmann
doaj   +1 more source

ALGORITHMIC ASPECTS OF ROMAN GRAPHS [PDF]

Journal of Algebraic Systems, 2021
Let $G=(V, E)$ be a graph. A set $S \subseteq V$ is called a dominating set of $G$ if for every $v\in V-S$ there is at least one vertex $u \in N(v)$ such that $u\in S$.
A. Poureidi
doaj   +1 more source

Counting the Number of Minimum Roman Dominating Functions of a Graph

CoRR, 2014
We provide two algorithms counting the number of minimum Roman dominating functions of a graph on n vertices in O(1.5673^n) time and polynomial space. We also show that the time complexity can be reduced to O(1.5014^n) if exponential space is used. Our result is obtained by transforming the Roman domination problem into other combinatorial problems on ...
Zheng Shi, Khee Meng Koh
openaire   +2 more sources

On interior Roman domination in graphs

Indonesian Journal of Combinatorics
Let G = (V(G), E(G)) be a non-complete graph and let ϕ:V(G)→{0,1,2} be a function on G. For each i ∈ {0, 1, 2}, let Vi={w ∈ V(G): ϕ(w)=i}.  A function ϕ=(V0, V1, V2) is an interior Roman dominating function (InRDF) on G if (i) for every v ∈ V0, there ...
Leomarich F. Casinillo
doaj   +1 more source

Roman domination in oriented trees

Electronic Journal of Graph Theory and Applications, 2021
Let D=(V,A) be a digraph of order n = |V|. A Roman dominating function of a digraph D is a function f : V  → {0,1,2} such that every vertex u for which f(u) = 0 has an in-neighbor v for which f(v) = 2.
Lyes Ouldrabah, Mostafa Blidia, Ahmed Bouchou   +2 more
doaj   +1 more source