Results 11 to 20 of about 6,662,662 (243)
A note on total domination [PDF]
Discrete Mathematics, 1984 A dominating [totally dominating] set is a subset D of the vertex set V(G) of a graph G with the property that for each \(x\in V(G)\setminus D\) [for each \(x\in V(G)]\) there exists \(y\in D\) adjacent to x. The domination number \(\gamma\) (G) [the total domination number \(\gamma_ t(G)]\) of G is the minimum number of vertices of a dominating ...
Robert B. Allan +2 more
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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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Total Version of the Domination Game [PDF]
Graphs and Combinatorics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael A. Henning +2 more
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Partial Total Domination in Hypergraphs
MathematicsThis paper establishes fundamental results for partial total domination in hypergraphs. We present tight bounds for the partial total domination number in k-uniform hypergraphs, demonstrate relationships with classical domination parameters, and provide ...
Abdulkafi Sanad, Chaoqian Li
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On upper bounds for total $k$-domination number via the probabilistic method [PDF]
, 2023 summary:For a fixed positive integer $k$ and $G=(V, E)$ a connected graph of order $n$, whose minimum vertex degree is at least $k$, a set $S\subseteq V$ is a total $k$-dominating set, also known as a $k$-tuple total dominating set, if every vertex $v\in
Cruz-Suárez, Hugo +2 more
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Total mixed domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2022 For a graph [Formula: see text] we call a subset [Formula: see text] a total mixed dominating set of G if each element of [Formula: see text] is either adjacent or incident to an element of S, and the total mixed domination number of G is the minimum ...
Adel P. Kazemi +2 more
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Total Domination in Generalized Prisms and a New Domination Invariant
Discussiones Mathematicae Graph Theory, 2021 In this paper we complement recent studies on the total domination of prisms by considering generalized prisms, i.e., Cartesian products of an arbitrary graph and a complete graph.
Tepeh Aleksandra
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Strong total domination and weak total domination in Mycielski’s graphs
Malaya Journal of Matematik, 2020 Let \(G=(V, E)\) be a graph. A set \(S \subseteq V\) is called a weak total dominating set (WTD-set) if each vertex \(v \in V-S\) is adjacent to a vertex \(u \in S\) with \(\operatorname{deg}(v)>\operatorname{deg}(u)\) and every vertex in \(S\) adjacent to a vertex in \(S\).
TUNÇEL GÖLPEK, HANDE, AYTAÇ, AYSUN
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Secure Total Domination in Rooted Product Graphs
Mathematics, 2020 In this article, we obtain general bounds and closed formulas for the secure total domination number of rooted product graphs. The results are expressed in terms of parameters of the factor graphs involved in the rooted product.
Abel Cabrera Martínez +2 more
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On graphs with equal total domination and Grundy total domination numbers
Aequationes mathematicae, 2021 A sequence $(v_1,\ldots ,v_k)$ of vertices in a graph $G$ without isolated vertices is called a total dominating sequence if every vertex $v_i$ in the sequence totally dominates at least one vertex that was not totally dominated by $\{v_1,\ldots , v_{i-1}\}$ and $\{v_1,\ldots ,v_k\}$ is a total dominating set of $G$.
Tanja Dravec +3 more
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