Results 31 to 40 of about 123,660 (292)
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
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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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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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Signed total Roman $k$-domination in directed graphs [PDF]
Communications in Combinatorics and Optimization, 2016 Let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Roman $k$-dominating function (STR$k$DF) on $D$ is a function $f:V(D)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N^{-}(v)}f(x)\ge k ...
N. Dehgard, L. Volkmann
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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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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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Relating the Outer-Independent Total Roman Domination Number with Some Classical Parameters of Graphs [PDF]
Mediterranean Journal of Mathematics, 2022 For a given graph G without isolated vertex we consider a function f:V(G)→{0,1,2}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage ...
Abel Cabrera Martínez +2 more
semanticscholar +6 more sources
Quasi total double Roman domination stability 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 [Formula: see text] if [Formula: see text], then the vertex v must have at least two neighbors ...
Saeed Kosari, Hanxin Jiang, M. Esmaeili
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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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