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Approximation Algorithms for Connected Dominating Sets
 Algorithmica
, 1996
"... The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size, whe ..."
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Cited by 366 (9 self)
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degree, and H is the harmonic function. This question also arises in relation to the traveling tourist problem, where one is looking for the shortest tour such that each vertex is either visited, or has at least one of its neighbors visited. We study a generalization of the problem when the vertices have
LARGE CLASSES OF INFINITE kCOPWIN GRAPHS
"... Abstract. While finite copwin finite graphs possess a good structural characterization, none is known for infinite copwin graphs. As evidence that such a characterization might not exist, we provide as large as possible classes of infinite graphs with finite cop number. More precisely, for each in ..."
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Cited by 3 (2 self)
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Abstract. While finite copwin finite graphs possess a good structural characterization, none is known for infinite copwin graphs. As evidence that such a characterization might not exist, we provide as large as possible classes of infinite graphs with finite cop number. More precisely, for each
Least squares ranking on graphs
, 2011
"... Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge values comprise the comparison data. The basic idea is very simple and old – come up with values on vertices such that their ..."
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Cited by 2 (1 self)
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Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge values comprise the comparison data. The basic idea is very simple and old – come up with values on vertices
The hat problem on cycles on at least nine vertices
"... The topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one gue ..."
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by an edge. The solution of the hat problem on a graph is known for trees and for the cycle C4. We solve the problem on cycles on at least nine vertices.
Global and regional climate changes due to black carbon,
 Nat. Geosci.,
, 2008
"... Figure 1: Global distribution of BC sources and radiative forcing. a, BC emission strength in tons per year from a study by Bond et al. Full size image (42 KB) Review Nature Geoscience 1, 221 227 (2008 Black carbon in soot is the dominant absorber of visible solar radiation in the atmosphere. Ant ..."
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Cited by 228 (5 self)
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clouds, with vertical extents of 3 to 5 km. Because of the combination of high absorption, a regional distribution roughly aligned with solar irradiance, and the capacity to form widespread atmospheric brown clouds in a mixture with other aerosols, emissions of black carbon are the second strongest
Vertical
"... profiling of precipitation using passive microwave observations: the main impediment and a proposed solution ..."
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profiling of precipitation using passive microwave observations: the main impediment and a proposed solution
Graph Laplacians and Least Squares on Graphs
"... Abstract—There are several classes of operators on graphs to consider in deciding on a collection of building blocks for graph algorithms. One class involves traditional graph operations such as breadth first or depth first search, finding connected components, spanning trees, cliques and other subg ..."
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subgraphs, operations for editing graphs and so on. Another class consists of linear algebra operators where the matrices somehow depend on a graph. It is the latter class of operators that this paper addresses. We describe a least squares formulation on graphs that arises naturally in problems of ranking
NOTES ON GRAPHS WITH LEAST EIGENVALUE AT LEAST −2
, 2012
"... A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectra ..."
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A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović
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