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Disjoint dominating and total dominating sets in graphs
Discrete Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Henning, Michael A. +3 more
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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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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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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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A Novel Hybrid Algorithm for Minimum Total Dominating Set Problem
Mathematics, 2019 The minimum total dominating set (MTDS) problem is a variant of the classical dominating set problem. In this paper, we propose a hybrid evolutionary algorithm, which combines local search and genetic algorithm to solve MTDS.
Fuyu Yuan +4 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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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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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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Partitioning a graph into a dominating set, a total dominating set, and something else [PDF]
Discussiones Mathematicae Graph Theory, 2010 A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, {\it Ars Comb.} {\bf 89} (2008), 159--162) implies that every connected graph of minimum degree at least three has a dominating set $D$ and a total dominating set $T$ which are disjoint.
Michael .A. Henning +2 more
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A Note on Non-Dominating Set Partitions in Graphs
Discussiones Mathematicae Graph Theory, 2016 A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S.
Desormeaux Wyatt J. +2 more
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