Results 41 to 50 of about 7,383,894 (206)
Quasi-total Roman reinforcement in graphs
AKCE International Journal of Graphs and Combinatorics, 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 ...
N. Ebrahimi +3 more
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Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight
Klein Douglas J. +1 more
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Perfect Domination Excellent Trees [PDF]
, 2012 A set D of vertices of a graph G is a perfect dominating set if every vertex in V \ D is adjacent to exactly one vertex in D. In this paper we introduce the concept of perfect domination excellent graph as a graph in which every vertex belongs to some ...
Sharada, B., Sharada B.
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Total Roman Domination of Kneser Graphs
, 2023 The total Roman domination number of a graph is the smallest possible sum of the weights 0, 1, and 2 applied to vertices of the graph that satisfy certain rules originating from Roman military strategy.
Stainsby, Cole +6 more
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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees
Mathematics, 2021 For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v ...
Xinyue Liu +3 more
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Total restrained Roman domination
, 2022 Published by Azabaijan Shahid Madani University, Azarshahr ...
Amjadi, Jafar +2 more
openaire +3 more sources
Total Roman domination edge-critical graphs [PDF]
Involve, a Journal of Mathematics, 2019 A total Roman dominating function on a graph $G$ is a function $% f:V(G)\rightarrow \{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ is adjacent to some vertex $u$ with $f(u)=2$, and the subgraph of $G$ induced by the set of all vertices $w$ such that $f(w)>0$ has no isolated vertices. The weight of $f$ is $Σ_{v\in V(G)}f(v)$.
Lampman, Chloe +2 more
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Total roman domination in digraphs
, 2021 Let D be a nite and simple digraph with vertex set V (D). A Roman dominating function (RDF) on a digraph D is a function f : V (D) → {0; 1; 2} satisfying the condition that every vertex v with f(v) = 0 has an in-neighbor u with f(u) = 2. The weight of an
Zhuang, Wei, Hu, Kangxiu, Hao, Guoliang
core
The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]
, 2009 The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar +3 more
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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
wiley +2 more sources