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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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Approximation hardness of dominating set problems in bounded degree graphs [PDF]
, 2008 We study approximation hardness of the Minimum Dominating Set problem and its variants in undirected and directed graphs. Using a similar result obtained by Trevisan for Minimum Set Cover we prove the first explicit approximation lower bounds for various
Chlebikova, Janka +4 more
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Some results on domination in annihilating-ideal graphs of commutative rings [PDF]
Journal of Hyperstructures. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are ...
Reza Taheri
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On Two Open Problems on Double Vertex-Edge Domination in Graphs
Mathematics, 2019 A vertex v of a graph G = ( V , E ) , ve-dominates every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is a double vertex-edge dominating set if every edge of E is ve-dominated by at least two
Fang Miao +5 more
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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Total Italian domatic number of graphs [PDF]
Computer Science Journal of Moldova, 2023 Let $G$ be a graph with vertex set $V(G)$. An \textit{Italian dominating function} (IDF) on a graph $G$ is a function $f:V(G)\longrightarrow \{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ is adjacent to a vertex $u$ with $f(u)=2$ or to two ...
Seyed Mahmoud Sheikholeslami +1 more
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Positive Influence Dominating Set in E-Learning Social Networks [PDF]
, 2011 In recent years, the development of E-learning is rapid. Learning efficiency can be greatly improved if E-learning users' social networks properties can be effectively utilized. However, the nodes in most research models are the same type.
Hua Wang +7 more
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Total Minimal Dominating Signed Graph [PDF]
, 2010 Cartwright and Harary considered graphs in which vertices represent persons and the edges represent symmetric dyadic relations amongst persons each of which designated as being positive or negative according to whether the nature of the relationship is ...
Reddy, Siva Kota, Vijay, S.
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A Note on the Locating-Total Domination in Graphs
Discussiones Mathematicae Graph Theory, 2017 In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Miller Mirka +4 more
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dib-lab/2022-dominating-set-differential-abundance-example: preprint version 1.0
, 2022 A reproducible example demonstrating an example workflow for performing dominating set differential abundance ...
Taylor Reiter
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