Results 31 to 40 of about 896 (158)
On Domatic and Total Domatic Numbers of Product Graphs
, 2021 A \emph{domatic} (\emph{total domatic}) \emph{$k$-coloring} of a graph $G$ is an assignment of $k$ colors to the vertices of $G$ such that each vertex contains vertices of all $k$ colors in its closed neighborhood (neighborhood). The \emph{domatic} (\emph{total domatic}) \emph{number} of $G$, denoted $d(G)$ ($d_t (G)$), is the maximum $k$ for which $G$
Francis, P., Rajendraprasad, Deepak
openaire +2 more sources
Signed star (k,k)-domatic number of a graph [PDF]
Opuscula Mathematica, 2014 Let \(G\) be a simple graph without isolated vertices with vertex set \(V(G)\) and edge set \(E(G)\) and let \(k\) be a positive integer. A function \(f:E(G)\longrightarrow \{-1, 1\}\) is said to be a signed star \(k\)-dominating function on \(G\) if ...
S. M. Sheikholeslami, L. Volkmann
doaj +1 more source
A novel approach to partial coverage in wireless sensor networks via the roman dominating set
IET Networks, Volume 11, Issue 2, Page 58-69, March 2022., 2022 Abstract One major challenge in deploying wireless sensor networks (WSN) in real‐world applications is minimising the energy consumption by the sensors while maintaining the coverage of the monitored field. However, many applications do not need full coverage of the monitored area all the time, which can help us reduce the network's energy consumption.
Fatemeh Ghaffari +2 more
wiley +1 more source
Common extremal graphs for three inequalities involving domination parameters [PDF]
Transactions on Combinatorics, 2017 Let $delta (G)$, $Delta (G)$ and $gamma(G)$ be the minimum degree, maximum degree and domination number of a graph $G=(V(G), E(G))$, respectively.
Vladimir Samodivkin
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The Roman domination and domatic numbers of a digraph [PDF]
Communications in Combinatorics and Optimization, 2019 Let $D$ be a simple digraph with vertex set $V$. A Roman dominating function (RDF) on a digraph $D$ is a function $f: V\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $v$ with $f(v)=0$ has an in-neighbor $u$ with $f(u)=2$. The weight
Z.Xie1, G. Hao, Sh. Wei
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Domination parameters with number 2: Interrelations and algorithmic consequences [PDF]
, 2018 In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination ...
Bonomo, Flavia +4 more
core +2 more sources
Families with infants: a general approach to solve hard partition problems [PDF]
, 2014 We introduce a general approach for solving partition problems where the goal is to represent a given set as a union (either disjoint or not) of subsets satisfying certain properties.
A. Björklund +14 more
core +1 more source
Coloring, location and domination of corona graphs [PDF]
, 2012 A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also an assignment of colors or labels to the vertices of a ...
Aguilar, A. Rondón +2 more
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10211 Abstracts Collection -- Flexible Network Design [PDF]
, 2010 From Monday 24.05.2010---Friday 28.05.2010, the Dagstuhl Seminar 10211 ``Flexible Network Design \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
+3 more
core +1 more source
The Roman Domatic Problem in Graphs and Digraphs: A Survey
Discussiones Mathematicae Graph Theory, 2022 In this paper, we survey results on the Roman domatic number and its variants in both graphs and digraphs. This fifth survey completes our works on Roman domination and its variations published in two book chapters and two other surveys.
Chellali Mustapha +3 more
doaj +1 more source