Results 31 to 40 of about 17,112 (263)
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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All graphs with paired-domination number two less than their order [PDF]
Opuscula Mathematica, 2013 Let \(G=(V,E)\) be a graph with no isolated vertices. A set \(S\subseteq V\) is a paired-dominating set of \(G\) if every vertex not in \(S\) is adjacent with some vertex in \(S\) and the subgraph induced by \(S\) contains a perfect matching.
Włodzimierz Ulatowski
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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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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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The Sierpiński domination number
Ars Mathematica ContemporaneaLet $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $gg'$ of $G$ there is an edge between copies $gH$ and $g'H$ of $H ...
Michael A. Henning +3 more
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On the domination number and the total domination number of Fibonacci cubes
Ars Mathematica Contemporanea, 2019 Summary: Fibonacci cubes are special subgraphs of the hypercube graphs. Their domination numbers and total domination numbers are obtained for some small dimensions by integer linear programming. For larger dimensions upper and lower bounds on these numbers are given.
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Results on the domination number and the total domination number of Lucas cubes
Ars Mathematica Contemporanea, 2020 Summary: Lucas cubes are the special subgraphs of Fibonacci cubes. For small dimensions, their domination numbers are obtained by direct search or integer linear programming. For larger dimensions some bounds on these numbers are given. In this work, we present the exact values of total domination number of small dimensional Lucas cubes and present ...
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Alternative Domination in Graphs
AKCE International Journal of Graphs and CombinatoricsSometimes while you are using the Internet, for example, via a Wi-Fi network from one of the companies, the Internet is suddenly cut off due to a malfunction at that point, which disrupts your important work on the Internet, so there is a need for ...
Ali Mohammed Sahal
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Discrete Mathematics, 2002 The dominating set of a digraph \(D\) is a set \(S\) of vertices such that for every \(v\not\in S\) there exists \(u\in S\) with \(uv\in A(D)\). The domination number of \(D\) is the cardinality of the smallest dominating set. The game domination number of an undirected graph \(G\) is the domination number of the digraph \(D\) obtained as a result of ...
Noga Alon +3 more
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Graphs with Total Domination Number Double of the Matching Number
Journal of New TheoryA subset $S$ of vertices of a graph $G$ with no isolated vertex is called a total dominating set of $G$ if each vertex of $G$ has at least one neighbor in the set $S$.
Selim Bahadır
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