Results 41 to 50 of about 9,635,811 (355)
On the Total Outer k-Independent Domination Number of Graphs
Mathematics, 2020 A set of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex in such a set. We say that a total dominating set D is a total outer k-independent dominating set of G if the maximum degree of the subgraph ...
A. Cabrera-Martínez +3 more
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Isolate and independent domination number of some classes of graphs
AKCE International Journal of Graphs and Combinatorics, 2019 In this paper we compute isolate domination number and independent domination number of some well known classes of graphs. Also a counter example is provided, which disprove the result on independent domination for Euler Totient Cayley graph proved by ...
Shilpa T. Bhangale, Madhukar M. Pawar
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Equitable eccentric domination in graphs
Ratio Mathematica, 2023 In this paper, we define equitable eccentric domination in graphs. An eccentric dominating set S ⊆ V (G) of a graph G(V, E) is called an equitable eccentric dominating set if for every v ∈ V − S there exist at least one vertex u ∈ V such that |d(v) − d(u)
A Riyaz Ur Rehman, A Mohamed Ismayil
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Characterization of Upper Detour Monophonic Domination Number
Cubo, 2020 This paper introduces the concept of \textit{upper detour monophonic domination number} of a graph. For a connected graph $G$ with vertex set $V(G)$, a set $M\subseteq V(G)$ is called minimal detour monophonic dominating set, if no proper subset of $M ...
M. Mohammed Abdul Khayyoom
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Graphs and CombinatoricsLet G be a bridgeless graph. An orientation of G is a digraph obtained from G by assigning a direction to each edge. The oriented diameter of G is the minimum diameter among all strong orientations of G.
P. Dankelmann +2 more
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Trees with vertex-edge Roman Domination number twice the domination number minus one
Proyecciones (Antofagasta), 2020 A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f (w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices.
H. Naresh Kumar, Y. B. Venkatakrishnan
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Reducing the domination number of graphs via edge contractions [PDF]
International Symposium on Mathematical Foundations of Computer Science, 2019 In this paper, we study the following problem: given a connected graph $G$, can we reduce the domination number of $G$ by at least one using $k$ edge contractions, for some fixed integer $k \geq 0$?
Esther Galby, Paloma T. Lima, B. Ries
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Graphs with equal domination and certified domination numbers [PDF]
Opuscula Mathematica, 2019 A set \(D\) of vertices of a graph \(G=(V_G,E_G)\) is a dominating set of \(G\) if every vertex in \(V_G-D\) is adjacent to at least one vertex in \(D\). The domination number (upper domination number, respectively) of \(G\), denoted by \(\gamma(G)\) (\(\Gamma(G)\), respectively), is the cardinality of a smallest (largest minimal, respectively ...
Magda Dettlaff +5 more
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Resolving domination number of helm graph and it’s operation
Journal of Physics: Conference Series, 2020 Let G be a connected graph. Dominating set is a set of vertices which each vertex D has at least one neighbor in G. The minimum cardinality of D is called the domination number G(γ(G)).
A. N. Hayyu +4 more
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Domination Number of Graphs with Minimum Degree Five [PDF]
Discussiones Mathematicae Graph Theory, 2019 We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method.
Csilla Bujt'as
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