Results 41 to 50 of about 129,130 (275)
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
doaj +1 more source
Survey on Roman {2}-Domination
MathematicsThe notion of Roman {2}-domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire.
Ahlam Almulhim +2 more
doaj +1 more source
On The Roman Domination Stable Graphs
Discussiones Mathematicae Graph Theory, 2017 A Roman dominating function (or just RDF) 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.
Hajian Majid, Rad Nader Jafari
doaj +1 more source
On the Roman Bondage Number of Graphs on surfaces [PDF]
, 2014 A Roman dominating function on a graph $G$ is a labeling $f : V(G) \rightarrow \{0, 1, 2\}$ such that every vertex with label $0$ has a neighbor with label $2$. The Roman domination number, $\gamma_R(G)$, of $G$ is the minimum of $\Sigma_{v\in V (G)} f(v)
Samodivkin, Vladimir
core
Rainbow domination and related problems on some classes of perfect graphs [PDF]
, 2015 Let $k \in \mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\emptyset$, $f(N(x)) =[k]$.
A Bertossi +23 more
core +2 more sources
Emergent Spin‐Glass Behavior in an Iron(II)‐Based Metal–Organic Framework Glass
Advanced Functional Materials, EarlyView.A one‐pot, solvent‐free synthesis yields an Fe2+‐based metal‐organic framework (MOF) glass featuring a continuous random network structure. The material exhibits spin‐glass freezing at 14 K, driven by topological‐disorder and short‐range magnetic frustration, showcasing the potential of MOF glasses as a plattform for cooperative magnetic phenomena in ...
Chinmoy Das +8 more
wiley +1 more source
Some Progress on the Double Roman Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex v, then v has at least two neighbors assigned 2 under f or one neighbor assigned 3 under f, and ...
Rad Nader Jafari, Rahbani Hadi
doaj +1 more source
Advanced Healthcare Materials, EarlyView.Here, we present a novel 3D cell patterning and culture platform. The “Floor‐Ceiling‐Chip” (FC‐Chip) consists of two opposing track‐etched membranes, creating a pseudo‐3D microenvironment for the cells in between. By providing the membranes with micropatterned cell‐adhesive islands of varying geometries and sizes, the FC‐Chip enables control over cell ...
Urandelger Tuvshindorj +10 more
wiley +1 more source
Triple Roman domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2022 For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)
Jafar Amjadi, Hakimeh Sadeghi
doaj
On the weak Roman domination number of lexicographic product graphs
, 2018 A vertex $v$ of a graph $G=(V,E)$ is said to be undefended with respect to a function $f: V \longrightarrow \{0,1,2\}$ if $f(v)=0$ and $f(u)=0$ for every vertex $u$ adjacent to $v$.
Pérez-Rosés, Hebert +2 more
core +1 more source