Results 11 to 20 of about 14,893,384 (293)
Total domination number of middle graphs
Electronic Journal of Graph Theory and Applications, 2022 A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set.
Farshad Kazemnejad +3 more
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Fair Total Domination Number in Cactus Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2021 For k ≥ 1, a k-fair total dominating set (or just kFTD-set) in a graph G is a total dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V\S. The k-fair total domination number of G, denoted by ftdk(G), is the minimum cardinality of a kFTD-set.
Hajian Majid, Rad Nader Jafari
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On the total domination number of total graphs [PDF]
Discussiones Mathematicae Graph TheorySummary: Let \(G\) be a graph with no isolated vertex. A set \(D\subseteq V(G)\) is a total dominating set of \(G\) if every vertex of \(G\) is adjacent to at least one vertex in \(D\). The total domination number of \(G\), denoted by \(\gamma_t(G)\), is the minimum cardinality among all total dominating sets of \(G\).
Abel Cabrera-Martínez +2 more
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Computing locating-total domination number in some rotationally symmetric graphs [PDF]
Science Progress, 2021 Let G = ( V , E ) be a connected graph. A locating-total dominating set in a graph G is a total dominating set S of a G , for every pair of vertices i , j ∈ V ( G ) ∖ S , such that N ( i ) ∩ S ≠ N ( j ) ∩ S .
Hassan Raza +3 more
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On the Secure Total Domination Number of Graphs [PDF]
Symmetry, 2019 A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex u ∈ V ( G ) \ D , there exists a vertex v ∈ D , which is adjacent to u, such that ( D \ { v } ) ∪ { u } is a total dominating set as well.
Abel Cabrera Martínez +2 more
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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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Trees with equal total and total restrained domination numbers [PDF]
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 ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number.
Hong-Yu Chen +2 more
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Disjunctive Total Domination Subdivision Number of Graphs
Fundamenta Informaticae, 2020 A set S ⊆ V (G) is a disjunctive total dominating set of G if every vertex has a neighbor in S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number is the minimum cardinality of a disjunctive total dominating set in G. We define the disjunctive total domination subdivision number of G as the minimum number of
Ciftci, Canan, Aytac, Vecdi
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On a Class of Graphs with Large Total Domination Number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Let $\gamma(G)$ and $\gamma_t(G)$ denote the domination number and the total domination number, respectively, of a graph $G$ with no isolated vertices. It is well-known that $\gamma_t(G) \leq 2\gamma(G)$.
Selim Bahadır, Didem Gözüpek
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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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