Results 11 to 20 of about 10,626,776 (155)
Bounds on the Double Italian Domination Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2022 For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
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Bounds on the total double Roman domination number of graphs [PDF]
Discussiones Mathematicae Graph Theory, 2023 Summary: 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 number and the numbers of support vertices and leaves, and we characterize all ...
Guoliang Hao +3 more
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Some Progress on the Double Roman Domination in Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2019 For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex v, then v has at least two neighbors assigned 2 under f or one neighbor assigned 3 under f, and ...
Rad Nader Jafari, Rahbani Hadi
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Upper Bounds for Double Roman Domination and [k]-Roman Domination of Cylindrical Graphs Cm☐Pn [PDF]
AxiomsRoman-type domination parameters form an important class of graph invariants that model protection and resource allocation problems on networks. Among them, [k]-Roman domination provides a unified framework that generalizes Roman, double Roman, and ...
Simon Brezovnik, Janez Žerovnik
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Calculating Modern Roman Domination of Fan Graph and Double Fan Graph [PDF]
Journal of Applied Sciences and Nanotechnology, 2022 This paper is concerned with the concept of modern Roman domination in graphs. A Modern Roman dominating function on a graph is labeling such that every vertex with label 0 is adjacent to two vertices; one of them of label 2 and the other of label 3 and ...
Saba Salah, Ahmed Omran, Manal Al-Harere
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Total double Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao +2 more
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Lower and upper bounds on independent double Roman domination in trees
Electronic Journal of Graph Theory and Applications, 2022 For a graph G = (V, E), a double Roman dominating function (DRDF) f : V → {0, 1, 2, 3} has the property that for every vertex v ∈ V with f(v)=0, either there exists a neighbor u ∈ N(v), with f(u)=3, or at least two neighbors x, y ∈ N(v) having f(x)=f(y ...
M. Kheibari +3 more
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The double Roman domination number of generalized Sierpiński graphs [PDF]
Discrete Mathematics, Algorithms and Applications, 2020 In this paper, we study the double Roman domination number of generalized Sierpiński graphs [Formula: see text]. More precisely, we obtain a bound for the double Roman domination number of [Formula: see text]. We also find the exact value of [Formula: see text].
Anu V., S. Aparna Lakshmanan
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On the D-differential of a graph
AKCE International Journal of Graphs and Combinatorics, 2022 Let [Formula: see text] be a graph of order n(G). For a subset S of V(G), the boundary of S is defined as [Formula: see text] where N(S) is the open neighborhood of S.
Kijung Kim
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Double Roman reinforcement number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 For a graph a double Roman dominating function is a function having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one ...
J. Amjadi, H. Sadeghi
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