Results 11 to 20 of about 9,767,318 (248)

Algorithmic Aspects of the Independent 2-Rainbow Domination Number and Independent Roman {2}-Domination Number [PDF]

Discussiones Mathematicae Graph Theory, 2022
A 2-rainbow dominating function (2RDF) of a graph G is a function g from the vertex set V (G) to the family of all subsets of {1, 2} such that for each vertex v with g(v) =∅ we have ∪u∈N(v) g(u) = {1, 2}.
Poureidi Abolfazl, Rad Nader Jafari
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Roman game domination subdivision number of a graph [PDF]

Transactions on Combinatorics, 2013
A {em Roman dominating function} on a graph $G = (V ,E)$ is a function $f : Vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. The {em weight} of a
Jafar Amjadi, Hossein Karami, Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +3 more
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Bounds on the Double Italian Domination Number of a Graph [PDF]

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

, 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 $G$.
Seyed Mahmoud Sheikholeslami, Chen, Xiaodan, Xiaodan Chen, Sheikholeslami, Seyed Mahmoud, Shouliu Wei, Guoliang Hao, Wei, Shouliu, Hao, Guoliang   +7 more
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Progress on Roman and Weakly Connected Roman Graphs

Mathematics, 2021
A graph G for which γR(G)=2γ(G) is the Roman graph, and if γRwc(G)=2γwc(G), then G is the weakly connected Roman graph. In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar
Joanna Raczek, Rita Zuazua
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The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]

, 2009
The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar, H.Abdollahzadeh Ahangar, Abdollahzadeh Ahangar, H., Pushpalatha L.   +3 more
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Triple Connected Domination Number of a Graph [PDF]

, 2012
The concept of triple connected graphs with real life application was introduced by considering the existence of a path containing any three vertices of a graph G.
Selvam Avadayappan, T.Subramanian, Joseph, Paulraj, J.Paulraj Joseph, G.Mahadevan, Avadayappan, Selvam, Subramanian, T., Mahadevan, G.   +7 more
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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
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Critical graphs with Roman domination number four

AKCE International Journal of Graphs and Combinatorics, 2020
A Roman domination function on a graph G is a function satisfying the condition that every vertex u for which r(u) = 0 is adjacent to at least one vertex v for which r(v) = 2.
A. Martínez-Pérez, D. Oliveros
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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
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