Results 31 to 40 of about 25,954 (258)
Closed formulas for the total Roman domination number of lexicographic product graphs
Ars Math. Contemp., 2021 Let G be a graph with no isolated vertex and f : V ( G ) → {0, 1, 2} a function. Let V i = { x ∈ V ( G ) : f ( x ) = i } for every i ∈ {0, 1, 2} . We say that f is a total Roman dominating function on G if every vertex in V 0 is adjacent to at least
Abel Cabrera Martínez +1 more
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On the signed strong total Roman domination number of graphs
Tamkang Journal of Mathematics, 2022 Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the condition
A. Mahmoodi +2 more
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Complexity of signed total $k$-Roman domination problem in graphs
AIMS Mathematics, 2021 Let $G$ be a simple graph with finite vertex set $V(G)$ and $S=\{-1,1,2\}$. A signed total Roman $k$-dominating function (STRkDF) on a graph $G$ is a function $f:V(G)\to S$ such that (i) any vertex $y$ with $f(y)=-1$ is adjacent to at least one vertex $t$
Saeed Kosari +4 more
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The signed (total) roman domination problem on some classes of planar graphs – convex polytopes [PDF]
Discret. Math. Algorithms Appl., 2023 In this paper we deal with the calculation of the signed (total) Roman domination numbers, $\gamma_{sR}$ and $\gamma_{stR}$ respectively, on a few classes of planar graphs from the literature.
Tatjana Zec +2 more
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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees [PDF]
Mathematics, 2021 For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v ...
Xinyue Liu +3 more
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Roman Edge Semi-Total Block Domination of a Graph
Asia Pacific Journal of Mathematics, 2018 Girish V.R., P. Usha
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Total Perfect Roman Domination [PDF]
Symmetry, 2023 A total perfect Roman dominating function (TPRDF) on a graph G=(V,E) is a function f from V to {0,1,2} satisfying (i) every vertex v with f(v)=0 is a neighbor of exactly one vertex u with f(u)=2; in addition, (ii) the subgraph of G that is induced by the vertices with nonzero weight has no isolated vertex. The weight of a TPRDF f is ∑v∈Vf(v). The total
Ahlam Almulhim
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Total Roman {2}-domination in graphs [PDF]
Quaestiones Mathematicae, 2019 23 ...
Suitberto Cabrera García +3 more
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Total Weak Roman Domination in Graphs [PDF]
Symmetry, 2019 Given a graph G = ( V , E ) , a function f : V → { 0 , 1 , 2 , ⋯ } is said to be a total dominating function if ∑ u ∈ N ( v ) f ( u ) > 0 for every v ∈ V , where N ( v ) denotes the open neighbourhood of v. Let V i = { x ∈ V : f ( x ) = i } . We say that a function f : V → { 0 , 1 , 2 }
Abel Cabrera Martínez +2 more
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Dominating the Direct Product of Two Graphs through Total Roman Strategies [PDF]
Mathematics, 2020 Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph of ...
Abel Cabrera Martínez +3 more
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