Results 61 to 70 of about 7,400,368 (352)
On the complexity of some hop domination parameters
Electronic Journal of Graph Theory and Applications, 2019 A hop Roman dominating function (HRDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of an HRDF f is the sum of its values
Nader Jafari Rad, Elahe Shabani
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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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Connected Dominating Sets [PDF]
, 2009 Wireless sensor networks (WSNs) are now widely used in many applications. However, routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other wireless networks. The concept of hierarchical routing is widely used to perform energy-efficient routing in WSNs.
Yiwei Wu, Yingshu Li
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The complexity of dominating set reconfiguration
, 2015 Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each ...
A Suzuki +11 more
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, 2016 This paper is devoted to the online dominating set problem and its variants on trees, bipartite, bounded-degree, planar, and general graphs, distinguishing between connected and not necessarily connected graphs. We believe this paper represents the first
Boyar, Joan +4 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
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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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Super Dominating Sets in Graphs [PDF]
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2015 7 pages, 4 ...
Lemańska, M. +3 more
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A Linear Kernel for Planar Total Dominating Set
, 2018 A total dominating set of a graph $G=(V,E)$ is a subset $D \subseteq V$ such that every vertex in $V$ is adjacent to some vertex in $D$. Finding a total dominating set of minimum size is NP-hard on planar graphs and W[2]-complete on general graphs when ...
Garnero, Valentin, Sau, Ignasi
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Dominating Sets in Projective Planes [PDF]
Journal of Combinatorial Designs, 2016 AbstractWe describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result that shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a dominating set in a projective plane of order is smaller than (i.e., twice the size of a Baer subplane ...
Héger, Tamás, Nagy, Zoltán Lóránt
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