Results 11 to 20 of about 16,468 (299)
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
openaire +3 more sources
Total Domination in Generalized Prisms and a New Domination Invariant [PDF]
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
doaj +2 more sources
Total domination versus paired domination [PDF]
Discussiones Mathematicae Graph Theory, 2012 A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by t.
Schaudt, Oliver
openaire +4 more sources
Total Domination Multisubdivision Number of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
doaj +2 more sources
Partial Total Domination in Hypergraphs [PDF]
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
doaj +2 more sources
Total connected domination game [PDF]
Opuscula Mathematica, 2021 The (total) connected domination game on a graph \(G\) is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices induce a ...
Csilla Bujtás +3 more
doaj +1 more source
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
doaj +1 more source
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
core +1 more source
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
doaj +1 more source
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
openaire +2 more sources