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Anarchism and non-domination [PDF]
, 2019 In this article we recover the classical anarchist deployment of republican tropes of non-domination, tyranny and slavery, to expose the conservative limits of the contemporary neo-Roman republican revival. For the anarchists, the modern nation state and
WAL Prichard (21872402) +1 more
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DOMINATION AND EDGE DOMINATION IN TREES [PDF]
Ural Mathematical Journal, 2020 Let \(G=(V,E)\) be a simple graph. A set \(S\subseteq V\) is a dominating set if every vertex in \(V \setminus S\) is adjacent to a vertex in \(S\).
B. Senthilkumar +2 more
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Domination, Eternal Domination, and Clique Covering
Discussiones Mathematicae Graph Theory, 2015 Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-
Klostermeyer William F., Mynhardt C.M.
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Discussiones Mathematicae Graph Theory, 2005 Summary: For a finite undirected graph \(G\) on \(n\) vertices two continuous optimization problems taken over the \(n\)-dimensional cube are presented and it is proved that their optimum values equal the domination number \(\gamma\) of \(G\). An efficient approximation method is developed and known upper bounds on \(\gamma\) are slightly improved.
Frank Göring, Jochen Harant
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On domination and independent domination numbers of a graph [PDF]
Discrete Mathematics, 1978 AbstractFor a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are obtained:Theorem. If G does not have an induced subgraph isomorphic to K1,3, then γ(G) = i(G).Corollary 1. For any graph G, γ(L(G))=i(L(G)), where L(G) is the line graph of G. (This extends
Robert B. Allan, Renu C. Laskar
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Relating 2-Rainbow Domination To Roman Domination
Discussiones Mathematicae Graph Theory, 2017 For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination
Alvarado José D. +2 more
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Upper paired domination versus upper domination [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A paired dominating set $P$ is a dominating set with the additional property that $P$ has a perfect matching. While the maximum cardainality of a minimal dominating set in a graph $G$ is called the upper domination number of $G$, denoted by $\Gamma(G ...
Hadi Alizadeh, Didem Gözüpek
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Domination versus edge domination [PDF]
Discrete Applied Mathematics, 2020 We propose the conjecture that the domination number $γ(G)$ of a $Δ$-regular graph $G$ with $Δ\geq 1$ is always at most its edge domination number $γ_e(G)$, which coincides with the domination number of its line graph. We prove that $γ(G)\leq \left(1+\frac{2(Δ-1)}{Δ2^Δ}\right)γ_e(G)$ for general $Δ\geq 1$, and $γ(G)\leq \left(\frac{7}{6}-\frac{1}{204 ...
Julien Baste +4 more
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Some Results on the Strong Roman Domination Number of Graphs [PDF]
Mathematics Interdisciplinary Research, 2020 Let G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is
Akram Mahmoodi +2 more
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Degree equitable restrained double domination in graphs
Electronic Journal of Graph Theory and Applications, 2021 A subset D ⊆ V(G) is called an equitable dominating set of a graph G if every vertex v ∈ V(G) \ D has a neighbor u ∈ D such that |dG(u)-dG(v)| ≤ 1. An equitable dominating set D is a degree equitable restrained double dominating set (DERD-dominating set)
Sunilkumar M Hosamani +3 more
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