Results 41 to 50 of about 1,279 (174)

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

Bounds on the locating Roman dominating number in trees [PDF]

, 2018
A Roman dominating function (or just RDF) on a graph $ G = (V, E) $ is a function $ f : V \rightarrow \{ 0, 1, 2 \} $ satisfying the condition that every vertex $u$ for which $ f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$.
Rahbani, Hadi, Hadi Rahbani, Nader Jafari Rad, Jafari Rad, Nader   +3 more
core   +1 more source

A Roman Domination Chain [PDF]

, 2016
For a graph (Formula presented.), a Roman dominating function (Formula presented.) has the property that every vertex (Formula presented.) with (Formula presented.) has a neighbor (Formula presented.) with (Formula presented.).
Haynes, Teresa W., Hedetniemi, Sandra M., Chellali, Mustapha, Hedetniemi, Stephen T., McRae, Alice A.   +4 more
core   +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

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

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 graphs [PDF]

, 2003
A Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2.
Paul A Dreyer, Ernie J Cockayne, Sandra M Hedetniemi, Stephen T Hedetniemi, Hedetniemi, Sandra M, Cockayne, Ernie J, Dreyer, Paul A, Hedetniemi, Stephen T   +7 more
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A note on the double Roman domination number of graphs [PDF]

, 2020
summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned $2$ under $f$ or one neighbor with $f(w)
Chen, Xue-Gang
core   +1 more source

On the complexity of some hop domination parameters

Electronic Journal of Graph Theory and Applications, 2019
A hop Roman dominating function (HRDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of an HRDF f is the sum of its values
Nader Jafari Rad, Elahe Shabani
doaj   +1 more source