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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
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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
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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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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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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
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On interior Roman domination in graphs
Indonesian Journal of CombinatoricsLet 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
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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 +2 more
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Restrained roman domination in graphs [PDF]
Transactions on Combinatorics, 2015 A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function 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. A set S V is a Restrained dominating set if every
Roushini Leely Pushpam +1 more
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Angewandte Chemie, EarlyView.Cement‐mimetic hydraulicity is realized in an organic polymer through a counterintuitive reaction in which a hydrophilic linear polymer reacts with water to undergo hydrophobization during curing via silatrane sol–gel chemistry. This polarity‐inverting curing process turns a water‐plasticized putty into a water‐tolerant rigid material, enabling ...
Rei Tokumitsu +3 more
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Angewandte Chemie, EarlyView.Increasing the density of isolated manganese (Mn) atoms in carbon nitride (CNx) photocatalysts does not continuously improve performance. Instead, beyond a critical loading, the polymer support reorganizes, altering charge‐carrier dynamics and oxygen activation while preserving atomic dispersion.
Viktoria Velichko +14 more
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