Results 71 to 80 of about 670,635 (308)
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
doaj +1 more source
Quasi-total Roman Domination in Graphs [PDF]
Results in Mathematics, 2019 15 ...
Cabrera García, Suitberto +2 more
openaire +5 more sources
On the total Roman domination in trees
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex.
Marzieh Soroudi +2 more
openaire +3 more sources
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
Italian, 2-rainbow and Roman domination numbers in middle graphs
RAIRO Oper. Res.Given a graph $G$, we consider the Italian domination number $\gamma_I(G)$, the $2$-rainbow domination number $\gamma_{r2}(G)$ and the Roman domination number $\gamma_R(G)$.
Kijung Kim
semanticscholar +1 more source
Roman domination in regular graphs
Discrete Mathematics, 2009 AbstractA Roman domination function on a graph G=(V(G),E(G)) is a function f:V(G)→{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. The weight of a Roman dominating function is the value f(V(G))=∑u∈V(G)f(u).
Yang Yuansheng, Jiang Baoqi, Fu Xueliang
openaire +2 more sources
Total Roman {3}-domination in Graphs [PDF]
Symmetry, 2020 For a graph G = ( V , E ) with vertex set V = V ( G ) and edge set E = E ( G ) , a Roman { 3 } -dominating function (R { 3 } -DF) is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that ∑ u ∈ N G ( v ) f ( u ) ≥ 3 , if f ( v ) = 0 , and ∑ u ∈ N G ( v ) f ( u
Shao, Zehui +2 more
openaire +3 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