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Large Language Models Utility for Rapid On-Site Evaluation in Interventional Pulmonology. [PDF]
Flaschner M +10 more
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Summary: In a graph \(G= (V,E)\) if we think of each vertex \(s\) as the possible location for a guard capable of protection each vertex in its closed neighborhood \(N[s]\), then ``domination'' requires every vertex to be protected. Thus, \(S\subset V(G)\) is a dominating set if \(\bigcup_{s\in s}N[s]= V(G)\).
Haynes, Teresa W., Slater, Peter J.
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A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The minimum cardinality of a paired dominating set of G is the paired domination number of G.
Desormeaux, Wyatt J. +2 more
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Induced-paired domination in graphs.
A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). If moreover the subset \(\langle S\rangle \) of \(G\) induced by \(S\) consists of independent edges, then \(S\) is an induced-paired dominating set in \(G\).
Studer, Daniel S. +2 more
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Paired-domination game played on cycles
Discrete Applied Mathematics, 2023This text further develops the graph domination game introduced in [\textit{B. Brešar} et al. SIAM J. Discrete Math. 24, No. 3, 979--991 (2010; Zbl 1223.05189)]. The version of the game studied involves two players, the Dominator and the Staller, who take turns choosing pairs of adjacent, unchosen vertices that dominate at least one vertex not ...
Michael Henning
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Paired-Domination Subdivision Numbers of Graphs
Graphs and Combinatorics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seyed Mahmoud Sheikholeslami +2 more
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Paired-Domination in Subdivided Star-Free Graphs
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul Dorbec, Sylvain Gravier
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The Outer-Paired Domination of Graphs
International Journal of Foundations of Computer Science, 2022In this paper, we introduce a new variant of domination called the outer-paired domination. For a graph [Formula: see text], an outer-paired dominating set [Formula: see text] is a dominating set of [Formula: see text] such that the induced subgraph of [Formula: see text] contains a perfect matching.
Chih-Yuan Lin +4 more
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Upper total domination versus upper paired-domination
Let G be a graph with no isolated vertices. A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S, while a paired-dominating set of G is a dominating set of vertices whose induced subgraph has a ...
Michael Henning, Paul Dorbec
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