Results 31 to 40 of about 43,554 (293)
Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
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Secure total domination in chain graphs and cographs
AKCE International Journal of Graphs and Combinatorics, 2020 Let G = (V,E) be a graph without isolated vertices. A subset D of vertices of G is called a total dominating set of G if for every there exists a vertex such that A total dominating set D of a graph G is called a secure total dominating set of G if for ...
Anupriya Jha
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Computing locating-total domination number in some rotationally symmetric graphs
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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Edge Dominating Sets and Vertex Covers
Discussiones Mathematicae Graph Theory, 2013 Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering ...
Dutton Ronald, Klostermeyer William F.
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Total Dominating Sets and Total Domination Polynomials of Square Of Paths
IOSR Journal of Mathematics, 2014 Let G= ( V , E ) be a simple connected graph. A set S V is a total dominating set of G if every vertex is adjacent to an element of S. Let Dt(Wn ,i) be the family of all total dominating sets of the graph Wn , n ≥ 3 with cardinality i, and let dt (Wn ,i) = │Dt (Wn 2 , i) │. In this paper we compute dt(Wn ,i),and obtain the polynomial Dt(Wn , x) = dt(Wn
T. Premala, C. Sekar
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Brief Announcement: Distributed Algorithms for Minimum Dominating Set Problem and Beyond, a New Approach [PDF]
, 2022 In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set (MTDS) problem. We propose a new idea to compute approximate MDS and MTDS. This new approach can be implemented in a distributed model or parallel model.
Alipour, Sharareh, Salari, Mohammadhadi
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Approximation hardness of dominating set problems in bounded degree graphs
, 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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Algorithmic complexity of secure connected domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a simple, undirected, and connected graph. A connected (total) dominating set is a secure connected (total) dominating set of G, if for each there exists such that and is a connected (total) dominating set of G. The minimum cardinality of a secure
J. Pavan Kumar +2 more
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Certain Properties of Domination in Product Vague Graphs With an Application in Medicine
Frontiers in Physics, 2021 The product vague graph (PVG) is one of the most significant issues in fuzzy graph theory, which has many applications in the medical sciences today.
Xiaolong Shi, Saeed Kosari
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A characterization of graphs with disjoint total dominating sets
Ars Mathematica Contemporanea, 2019 Summary: A set \(S\) of vertices in a graph \(G\) is a total dominating set of \(G\) if every vertex is adjacent to a vertex in \(S\). A fundamental problem in total domination theory in graphs is to determine which graphs have two disjoint total dominating sets.
Michael A. Henning, Iztok Peterin
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