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Bounds on the Double Italian Domination Number of a Graph
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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Weak signed Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A weak signed Roman dominating function (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N[v]}f(x)\ge 1$ for each $v\in V(G)$, where $N[v]$ is the closed ...
Lutz Volkmann
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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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The 2-domination and Roman domination numbers of grid graphs
Discrete Mathematics & Theoretical Computer Science, 2019 We investigate the 2-domination number for grid graphs, that is the size of a smallest set $D$ of vertices of the grid such that each vertex of the grid belongs to $D$ or has at least two neighbours in $D$. We give a closed formula giving the 2-domination number of any $n \!\times\! m$ grid, hereby confirming the results found by Lu and Xu, and Shaheen
Rao, Michaël, Talon, Alexandre
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The Number of Minimum Dominating Sets in Pn × P2 [PDF]
, 2010 A set S of vertices in a graph G is said to be a Smarandachely k-dominating set if each vertex of G is dominated by at least k vertices of S.
Kishori P. Narayankar +5 more
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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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Angewandte Chemie, EarlyView.Cement‐mimetic hydraulicity is realized in an organic polymer through a counterintuitive reaction in which a hydrophilic linear polymer reacts with water to undergo hydrophobization during curing via silatrane sol–gel chemistry. This polarity‐inverting curing process turns a water‐plasticized putty into a water‐tolerant rigid material, enabling ...
Rei Tokumitsu +3 more
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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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Perfect Domination, Roman Domination and Perfect Roman Domination in Lexicographic Product Graphs
, 2022 The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs.
Cabrera Martinez, A.; Garcia-Gomez, C.; Rodriguez-Velazquez, J. A.;
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THE ROMAN BONDAGE NUMBER OF A DIGRAPH
, 2016 Let D=(V,A)D=(V,A) be a finite and simple digraph. A Roman dominating function on DD is a labeling f:V(D)→{0,1,2}f:V(D)→{0,1,2} such that every vertex with label 0 has an in-neighbor with label 2.
Sheikholeslami, Seyed Mahmoud;Dehgardi, Nasrin;Volkmann, Lutz;Meierling, Dirk +4 more
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