Results 81 to 90 of about 776,655 (324)
On the co-Roman domination in graphs
Discussiones Mathematicae Graph Theory, 2019 Let G = (V, E) be a graph and let f : V (G) → {0, 1, 2} be a function. A vertex v is said to be protected with respect to f, if f(v) > 0 or f(v) = 0 and v is adjacent to a vertex of positive weight. The function f is a co-Roman dominating function if (i) every vertex in V is protected, and (ii) each v ∈ V with positive weight has a neighbor u ∈ V with ...
Zehui Shao +4 more
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Advanced Functional Materials, EarlyView.This study explores the use of fluorinated copolymers with varying fluorophilic side chain lengths to enhance PFAS affinity. The integration of electrochemical techniques demonstrates enhanced adsorbent regeneration, with molecular dynamics simulations providing insight into the molecular‐level interactions involved.
Anaira Román Santiago +7 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
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
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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
DOUBLE ROMAN DOMINATION NUMBER OF MIDDLE GRAPH
South East Asian J. of Mathematics and Mathematical Sciences, 2022 For any graph G(V, E), a function f : V (G) 0, 1, 2, 3 is called Double Roman dominating function (DRDF) if the following properties holds, If f (v) = 0, then there exist two vertices v1, v2 ∈ N (v) for which f (v1) = f (v2) = 2 or there exist ...
Shailaja S. Shirkol +2 more
semanticscholar +1 more source
Retrospective Review on Reticular Materials: Facts and Figures Over the Last 30 Years
Advanced Materials, EarlyView.To shape the future course of research in reticular materials, this work reflects on the progress over the past 30 years, complemented by input from the community of 228 active researchers through a global, crowdsourced survey: ranging from demographics, how it works, publish and interact, to highlights on both academic and industrial milestones, as ...
Aamod V. Desai +8 more
wiley +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
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
On the Outer-Independent Roman Domination in Graphs [PDF]
Symmetry, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. Let Vi={v∈V(G):f(v)=i} for every i∈{0,1,2}. The function f is an outer-independent Roman dominating function on G if V0 is an independent set and every vertex in V0 is adjacent to at least one vertex in V2.
Cabrera Martínez, Abel +3 more
openaire +2 more sources