Results 41 to 50 of about 1,605,758 (310)
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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Complexity and Exact Values for [k]-Roman and Strong Roman Domination for Specific Graph Families
MathematicsMotivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks.
Juan Carlos Valenzuela-Tripodoro +3 more
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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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Super Hop Roman Domination in Graphs
European Journal of Pure and Applied MathematicsLet $G = (V(G), E(G))$ be a simple undirected graph. A function $f:V(G)\rightarrow \{0,1,2\}$ is a super hop Roman dominating function (SHRDF) on $G$ if for every $v\in V(G)$ with $f(v)=0$, there exist $w, u \in V(G)$ with $f(w) = 2$ and $f(u) \ne 0 ...
L. Casinillo, Sergio Canoy
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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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On the Total Version of Triple Roman Domination in Graphs
MathematicsIn this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from {0,1,2,3,4} to the vertices of a graph such that every vertex is protected by at least three units either on itself or ...
Juan Carlos Valenzuela-Tripodoro +3 more
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Annals of Mathematics and Computer ScienceA graph associated to a finite group is a way to analyze some properties of a group graphically. Many graphs of groups have been constructed according to the properties of the groups such as the commuting and non-commuting graphs.
Akram Alqesmah, Deepak Gangabylaiah
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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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A note on the independent roman domination in unicyclic graphs [PDF]
Opuscula Mathematica, 2012 A Roman dominating function (RDF) on a graph \(G = (V;E)\) is a function \(f : V \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\).
Mustapha Chellali, Nader Jafari Rad
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Molecular Basis of NPY Recognition and Ligand Selectivity at the Neuropeptide Y5 Receptor
Angewandte Chemie, EarlyView.Here, we present the first active structure of the neuropeptide Y5 receptor (NPY5R) in complex with its endogenous ligand NPY and the Gi1 protein. The cryo‐electron microscopy structure, validated by extensive mutagenesis studies, gives important insights into the molecular mechanisms underlying ligand binding and receptor activation.
Lisa Christin Peuker +8 more
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