Results 71 to 80 of about 7,293,468 (349)
Efficient and Perfect domination on circular-arc graphs [PDF]
, 2015 Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$.
Lin, Min Chih +2 more
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Eternal Domination: Criticality and Reachability
Discussiones Mathematicae Graph Theory, 2017 We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached.
Klostermeyer William F. +1 more
doaj +1 more source
A Fast Local Search Algorithm for Minimum Weight Dominating Set Problem on Massive Graphs
International Joint Conference on Artificial Intelligence, 2018 The minimum weight dominating set (MWDS) problem is NP-hard and also important in many applications. Recent heuristic MWDS algorithms can hardly solve massive real world graphs effectively.
Yiyuan Wang +3 more
semanticscholar +1 more source
Minimal graphs with disjoint dominating and paired-dominating sets
Discussiones Mathematicae Graph Theory, 2021 A subset $D\subseteq V_G$ is a dominating set of $G$ if every vertex in $V_G-D$ has a~neighbor in $D$, while $D$ is a paired-dominating set of $G$ if $D$ is a~dominating set and the subgraph induced by $D$ contains a perfect matching. A graph $G$ is a $D\!P\!D\!P$-graph if it has a pair $(D,P)$ of disjoint sets of vertices of $G$ such that $D$ is a ...
Michael A. Henning, Jerzy Topp
openaire +7 more sources
Fast algorithms for min independent dominating set
, 2009 We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm
D.S. Johnson +9 more
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False alarms in fault-tolerant dominating sets in graphs [PDF]
Opuscula Mathematica, 2012 We develop the problem of fault-tolerant dominating sets (liar's dominating sets) in graphs. Namely, we consider a new kind of fault - a false alarm.
Mateusz Nikodem
doaj +1 more source
Domination alteration sets in graphs
Discrete Mathematics, 1983 AbstractThe domination number α(G) of a graph G is the size of a minimum dominating set, i.e., a set of points with the property that every other point is adjacent to a point of the set. In general α(G) can be made to increase or decrease by the removal of points from G. Our main objective is the study of this phenomenon.
Bauer, Douglas +3 more
openaire +4 more sources
Power domination in maximal planar graphs [PDF]
, 2019 Power domination in graphs emerged from the problem of monitoring an electrical system by placing as few measurement devices in the system as possible. It corresponds to a variant of domination that includes the possibility of propagation.
Dorbec, Paul +2 more
core +1 more source
Population Ecology, EarlyView.Population size and dynamics fundamentally shape speciation by influencing genetic drift, founder events, and adaptive potential. Small populations may speciate rapidly due to stronger drift, whereas large populations harbor more genetic diversity, which can alter divergence trajectories. We highlight theoretical models that incorporate population size
Ryo Yamaguchi +3 more
wiley +1 more source
Proper 3-Dominating Sets in Graphs
MathematicsA dominating set is a classic concept that is widely used in road safety, disaster rescue operations, and chemical graphs. In this paper, we introduce a variation of the dominating set: the proper 3-dominating set.
Danmei Chen, Shuangjie Cai
doaj +1 more source