Results 21 to 30 of about 124,108 (282)
Total Roman domination in graphs
Applicable Analysis and Discrete Mathematics, 2016 A Roman dominating function on a graph 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 f is the sum, ΣuV(G) f(u), of the weights of the vertices.
Hossein Ahangar Abdollahzadeh +3 more
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On the (total) Roman domination in Latin square graphs
AIMS Mathematics, 2023 Latin square, also known as Latin square matrix, refers to a kind of $ n\times n $ matrix, in which there are exactly $ n $ different symbols and each symbol appears exactly once in each row and column.
Chang-Xu Zhang +2 more
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Quasi total double Roman domination in graphs
AKCE International Journal of Graphs and CombinatoricsA quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari +4 more
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Improved Total Domination and Total Roman Domination in Unit Disk Graphs
arXiv.orgLet $G=(V, E)$ be a simple undirected graph with no isolated vertex. A set $D_t\subseteq V$ is a total dominating set of $G$ if $(i)$ $D_t$ is a dominating set, and $(ii)$ the set $D_t$ induces a subgraph with no isolated vertex. The total dominating set of minimum cardinality is called the minimum total dominating set, and the size of the minimum ...
Rout, Sasmita, Das, Gautam Kumar
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Computational Complexity of Outer-Independent Total and Total Roman Domination Numbers in Trees
IEEE Access, 2018 An outer-independent total dominating set (OITDS) of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent.
Zepeng Li +4 more
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Roman Edge Semi-Total Block Domination of a Graph
Asia Pacific Journal of Mathematics, 2018 Summary: A graph \(G=(V,E)\), semi-total block graph \(T_b(G)=H\), whose set of vertices is the union of the set of vertices and blocks of \(G\) in whose two vertices are adjacent if and only if the corresponding vertices and blocks of \(G\) are adjacent or the corresponding members are incident.
Girish V.R., P. Usha
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Outer-independent total Roman domination in graphs
Discrete Applied Mathematics, 2019 Given a graph $G$ with vertex set $V$, a function $f:V\rightarrow \{0,1,2\}$ is an outer-independent total Roman dominating function on $G$ if \begin{itemize} \item every vertex $v\in V$ for which $f(v)=0$ is adjacent to at least one vertex $u\in V$ such that $f(u)=2$, \item every vertex $x\in V$ for which $f(x)\ge 1$ is adjacent to at least one vertex
Abel Cabrera Martínez +2 more
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Signed total double Roman dominating functions in graphs
AKCE International Journal of Graphs and CombinatoricsA signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w
L. Shahbazi +2 more
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The signed (total) Roman domination problem on some classes of planar graphs - Convex polytopes [PDF]
Discret. Math. Algorithms Appl., 2021 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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Several Roman domination graph invariants on Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination.
Tatjana Zec, Milana Grbić
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