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Twin-width III: Max Independent Set, Min Dominating Set, and Coloring
International Colloquium on Automata, Languages and ProgrammingWe recently introduced the notion of twin-width, a novel graph invariant, and showed that first-order model checking can be solved in time f ( d, k ) n for n -vertex graphs given with a witness that the twin-width is at most d , called d -contraction ...
Édouard Bonnet +4 more
semanticscholar +1 more source
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
doaj +1 more source
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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New results on metric-locating-dominating sets of graphs [PDF]
, 2016 A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number.
González, Antonio +2 more
core +3 more sources
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
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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Approximating Minimum Independent Dominating Sets in Wireless Networks [PDF]
, 2007 We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth.
Hurink, J.L., Nieberg, T.
core +6 more sources
On Locating-Dominating Set of Regular Graphs
Journal of Mathematics, 2021 Let G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈
Anuwar Kadir Abdul Gafur +1 more
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Location-domination in line graphs
, 2016 A set $D$ of vertices of a graph $G$ is locating if every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \cap D \neq N(v) \cap D$, where $N(u)$ denotes the open neighborhood
Foucaud, Florent, Henning, Michael A.
core +3 more sources
Clinical Insights Into Hypercalcemia of Malignancy in Childhood
Pediatric Blood &Cancer, EarlyView.ABSTRACT Hypercalcemia of malignancy (HCM) is a rare but life‐threatening metabolic emergency in children that occurs in less than 1% of pediatric cancer cases, with a reported incidence ranging from 0.4% to 1.0% across different studies. While it is observed in 10%–20% of adult malignancies, pediatric HCM remains relatively uncommon.
Hüseyin Anıl Korkmaz
wiley +1 more source