Results 81 to 90 of about 670,635 (308)
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 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 Healthcare Materials, EarlyView.A tunable methacrylated decellularized bone matrix hydrogel (dECM‐MA) is developed to support 3D culture of human osteoblasts. The hydrogel preserves bone‐specific ECM cues and allows precise control over mechanical properties. This system provides a customizable platform for studying osteogenic differentiation and modeling bone tissue environments for
Minne Dekker +5 more
wiley +1 more source
Strong equality of Roman and perfect Roman Domination in trees
RAIRO Oper. Res., 2022 A Roman dominating function (RD-function) on a graph $G = (V, E)$ is a function $f: V \longrightarrow \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$.
Z. Shao +4 more
semanticscholar +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
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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
A note on Roman domination in graphs
Discrete Mathematics, 2006 AbstractLet G=(V,E) be a simple graph. A subset S⊆V is a dominating set of G, if for any vertex u∈V-S, there exists a vertex v∈S such that uv∈E. The domination number of G, γ(G), equals the minimum cardinality of a dominating set. A Roman dominating function on graph G=(V,E) is a function f:V→{0,1,2} satisfying the condition that every vertex v for ...
Xin Chen, Hua-Ming Xing, Xue-Gang Chen
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Advanced Materials, EarlyView.A biphasic Ni‐MXene quantum‐confined nanostructure (Ni‐MJQD) serves as a Janus platform, simultaneously achieving high‐performance energy storage and efficient catalytic oxidation. The unique architecture enables superior energy storage performance and selective benzyl alcohol oxidation‐symbolizing “one stone, two birds” for sustainable energy and ...
Lagnamayee Mohapatra +5 more
wiley +1 more source
Outer Independent Double Roman Domination Stability in Graphs
Ars Comb.An outer independent double Roman dominating function (OIDRDF) on a graph G is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that (i) if f ( v ) = 0 , then the vertex v must have at least two neighbors assigned 2 under f or one neighbor ...
S. Sheikholeslami +2 more
semanticscholar +1 more source
Roman dominating influence parameters
Discrete Mathematics, 2007 AbstractA function f:V(G)→{0,1,2} is a Roman dominating function for a graph G=(V,E) if for every vertex v with f(v)=0, there exists a vertex w∈N(v) with f(w)=2. Emperor Constantine had the requirement that an army or legion could be sent from its home to defend a neighboring location only if there was a second army which would stay and protect the ...
Peter J. Slater, Robert R. Rubalcaba
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