Results 31 to 40 of about 1,521,521 (318)
Bounds on the Locating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2020 Given a graph G = (V, E) with no isolated vertex, a subset S of V is called a total dominating set of G if every vertex in V has a neighbor in S. A total dominating set S is called a locating-total dominating set if for each pair of distinct vertices u ...
Wang Kun, Ning Wenjie, Lu Mei
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Relating the total domination number and the annihilation number of cactus graphs and block graphs
Ars Math. Contemp., 2018 The total domination number γ t ( G ) of a graph G is the order of a smallest set D ⊆ V ( G ) such that each vertex of G is adjacent to some vertex in D .
Csilla Bujtás, Marko Jakovac
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Lower bounds for the Zagreb indices of trees with given total domination number and its applications in QSPR studies of alkanes. [PDF]
Sci RepManuel M, Parthiban A.
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Bounding the k-rainbow total domination number [PDF]
Discrete Mathematics, 2020 Recently the notion of $k$-rainbow total domination was introduced for a graph $G$, motivated by a desire to reduce the problem of computing the total domination number of the generalized prism $G \Box K_k$ to an integer labeling problem on $G$. In this paper we further demonstrate usefulness of the labeling approach, presenting bounds on the rainbow ...
Kerry Ojakian +2 more
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Locating-Total Domination Number of Cacti Graphs [PDF]
Mathematical Problems in Engineering, 2020 For a connected graph J, a subset W ⊆ V J is termed as a locating-total dominating
Jianxin Wei +3 more
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The Domination Parameters on a kind of the regular honeycomb structure [PDF]
Computer Science Journal of Moldova, 2022 The honeycomb mesh, based on hexagonal structure, has enormous applications in chemistry and engineering. A major challenge in this field is to understand the unique properties of honeycomb structures, which depend on their properties of topology. One
Fateme Movahedi +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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New Bounds on the Double Total Domination Number of Graphs
Bulletin of the Malaysian Mathematical Sciences Society, 2021 Let G be a graph of minimum degree at least two. A set $$D\subseteq V(G)$$ D ⊆ V ( G ) is said to be a double total dominating set of G if $$|N(v)\cap D|\ge 2$$ | N ( v ) ∩ D | ≥ 2 for every vertex $$v\in V(G)$$ v ∈ V ( G ) .
A. Cabrera-Martínez +1 more
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Total 2-rainbow domination numbers in trees
Discussiones Mathematicae Graph Theory, 2021 A function \(f:V(G) \rightarrow 2^{\{1,2\}}\) is a \(2\)-rainbow dominating function (2RDF) of a graph \(G\) if for every vertex \(v\) with \(f(v) = \emptyset\) we have \(\cup_{u\in N(v)} f(u) = \{1,2\}\). A 2RDF \(f\) is a total 2-rainbow dominating function (T2RDF) if the subgraph induced by the vertices \(v\) with \(f(v) \ne \emptyset\) has no ...
Ahangar H. Abdollahzadeh +4 more
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Hop total Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this article, we initiate a study of hop total Roman domination defined as follows: a hop total Roman dominating function (HTRDF) on a graph [Formula: see text] is a function [Formula: see text] such that for every vertex u with f(u) = 0 there exists ...
H. Abdollahzadeh Ahangar +3 more
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