Results 11 to 20 of about 9,286,296 (115)
Double Roman and double Italian domination [PDF]
, 2023 Let $G$ be a graph with vertex set $V(G)$. A double Roman dominating function (DRDF) on a graph $G$ is a function \( f:V(G)\longrightarrow\{0,1,2,3\} \) that satisfies the following conditions: (i) If $f(v)=0$, then $v$ must have a neighbor $w$ with $f(w)
Volkmann, Lutz, Lutz Volkmann
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From Total Roman Domination in Lexicographic Product Graphs to Strongly Total Roman Domination in Graphs [PDF]
, 2021 [EN] Let G be a graph with no isolated vertex and let N (v) be the open neighbourhood of v is an element of V (G). Let f : V (G) -> {0, 1, 2} be a function and V-i = {v is an element of V (G) : f (v) = i} for every i is an element of{0, 1, 2}.
Ana Almerich-Chulia +7 more
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A note on the double Roman domination number of graphs [PDF]
, 2020 summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned $2$ under $f$ or one neighbor with $f(w)
Chen, Xue-Gang
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Restrained double Roman domination of a graph
, 2022 For a graph G = (V, E), a restrained double Roman dominating function is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0, then the vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(
Doost Ali Mojdeh +2 more
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On Roman, Global and Restrained Domination in Graphs [PDF]
, 2010 In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible.
Zverovich, Vadim +3 more
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Quasi-total Roman reinforcement in graphs
, 2023 A quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex ...
M. Chellali +3 more
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Bounds on the total double Roman domination number of graphs [PDF]
, 2023 Let $G$ be a simple graph with no isolated vertex and let $\gamma_{tdR}(G)$ be the total double Roman domination number of $G$. In this paper, we present lower and upper bounds on $\gamma_{tdR}(G)$ of a graph $G$ in terms of the order, open packing ...
Xie, Zhihong +7 more
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Maximal double Roman domination in graphs
, 2022 A maximal double Roman dominating function (MDRDF) on a graph G = (V, E) is a function f:V(G)→{0,1,2,3} such that (i) every vertex v with f(v)=0 is adjacent to least two vertices assigned 2 or to at least one vertex assigned 3, (ii) every vertex v with f(
Chellali, M. +3 more
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Total Perfect Roman Domination
, 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
Ahlam Almulhim
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On the Outer Independent Total Double Roman Domination in Graphs [PDF]
, 2023 A double Roman dominating function (DRDF) on a graph G=(V, E) is a function f:V→ {0,1,2,3} satisfying (i) if f(v)=0, then there must be at least two neighbors assigned 2 under f or one neighbor w with f(w)=3; and (ii) if f(v)=1 then v must be adjacent to
H. Abdollahzadeh Ahangar +7 more
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