Results 51 to 60 of about 11,159 (184)
Total restrained domination numbers of trees
Discrete Mathematics, 2008 AbstractFor a given connected graph G=(V,E), a set Dtr⊆V(G) is a total restrained dominating set if it is dominating and both 〈Dtr〉 and 〈V(G)-Dtr〉 do not contain isolate vertices. The cardinality of the minimum total restrained dominating set in G is the total restrained domination number and is denoted by γtr(G).
Joanna Raczek, Joanna Cyman
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On Grundy Total Domination Number in Product Graphs
Discussiones Mathematicae Graph Theory, 2021 A longest sequence (v1, . . ., vk) of vertices of a graph G is a Grundy total dominating sequence of G if for all i, N(υj)\∪j=1i-1N(υj)≠∅N({\upsilon _j})\backslash \bigcup\nolimits_{j = 1}^{i - 1} {N({\upsilon _j})} \ne \emptyset .
Brešar Boštjan +8 more
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Total domination subdivision numbers of graphs
Discussiones Mathematicae Graph Theory, 2004 Summary: A set \(S\) of vertices in a graph \(G=(V,E)\) is a total dominating set of \(G\) if every vertex of \(V\) is adjacent to a vertex in \(S\). The total domination number of \(G\) is the minimum cardinality of a total dominating set of \(G\). The total domination subdivision number of \(G\) is the minimum number of edges that must be subdivided (
Michael A. Henning +2 more
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New Bounds on the Signed Total Domination Number of Graphs
Discussiones Mathematicae Graph Theory, 2016 In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥
Moghaddam Seyyed Mehdi Hosseini +3 more
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Trees with equal total and total restrained domination numbers
Discussiones Mathematicae Graph Theory, 2008 For a graph G = (V; E), a set S V (G) is a total dominating set if it is dominating and both hSi has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S V (G) is a total restrained dominating set if it is total dominating and hV (G) Si has no isolated vertices.
Hong-Yu Chen +2 more
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Total $k$-rainbow domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2020 A total $k$-rainbow dominating function (T$k$RDF) of $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,\ldots,k\}$ such that (i) for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u \in N(v ...
Rana Khoeilar +3 more
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On the domination number and the total domination number of Fibonacci cubes
Ars Mathematica Contemporanea, 2019 Fibonacci cubes are special subgraphs of the hypercube graphs. Their domination numbers and total domination numbers are obtained for some small dimensions by integer linear programming. For larger dimensions upper and lower bounds on these numbers are given.
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Further Results on Total Edge-Vertex Domination
Journal of Mathematics, 2022 Total edge-vertex domination is a new total domination-type parameter. In this paper, the author shows that determining the total edge-vertex domination number in bipartite planar graphs is NP-complete.
Abdulgani Şahin
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On total domination subdivision numbers of trees
Discussiones Mathematicae Graph Theory15 pages, 7 ...
Michael A. Henning, Jerzy Topp
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On the Total Outer k-Independent Domination Number of Graphs
Mathematics, 2020 A set of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex in such a set. We say that a total dominating set D is a total outer k-independent dominating set of G if the maximum degree of the subgraph ...
Abel Cabrera-Martínez +3 more
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