Results 21 to 30 of about 13,369 (211)
On the Quasi-Total Roman Domination Number of Graphs
Mathematics, 2021 Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems ...
Abel Cabrera Martínez +2 more
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Neighbourhood total domination in graphs [PDF]
Opuscula Mathematica, 2011 Let \(G = (V,E)\) be a graph without isolated vertices. A dominating set \(S\) of \(G\) is called a neighbourhood total dominating set (ntd-set) if the induced subgraph \(\langle N(S)\rangle\) has no isolated vertices.
S. Arumugam, C. Sivagnanam
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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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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 +5 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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On the {2}-domination number of graphs
AIMS Mathematics, 2022 Let $ G $ be a nontrivial graph and $ k\geq 1 $ an integer. Given a vector of nonnegative integers $ w = (w_0, \ldots, w_k) $, a function $ f: V(G)\rightarrow \{0, \ldots, k\} $ is a $ w $-dominating function on $ G $ if $ f(N(v))\geq w_i $ for every $ v\
Abel Cabrera-Martínez +1 more
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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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An upper bound on the total outer-independent domination number of a tree [PDF]
Opuscula Mathematica, 2012 A total outer-independent dominating set of a graph \(G=(V(G),E(G))\) is a set \(D\) of vertices of \(G\) such that every vertex of \(G\) has a neighbor in \(D\), and the set \(V(G) \setminus D\) is independent.
Marcin Krzywkowski
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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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Ars Mathematica Contemporanea, 2021 A subset of vertices in a graph is called a total dominating set if every vertex of the graph is adjacent to at least one vertex of this set. A total dominating set is called minimal if it does not properly contain another total dominating set. In this paper, we study graphs whose all minimal total dominating sets have the same size, referred to as ...
Ekim Aşıcı, Tınaz +2 more
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