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Vertexcolouring Edgeweightings
 COMBINATORICA
, 2007
"... A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted cv, is ∑ w(e). We show that the edges of every graph that e∋v does not contain a component isomorphic to K2 can be weighted from the set {1,...,30} such that in the resulting vertex ..."
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Cited by 11 (0 self)
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A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted cv, is ∑ w(e). We show that the edges of every graph that e∋v does not contain a component isomorphic to K2 can be weighted from the set {1,...,30} such that in the resulting
Circular colorings of edgeweighted graphs
 J. Graph Theory
, 2003
"... The notion of (circular) colorings of edgeweighted graphs is introduced. This notion generalizes the notion of (circular) colorings of graphs, the channel assignment problem, and several other optimization problems. For instance, its restriction to colorings of weighted complete graphs corresponds ..."
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Cited by 12 (4 self)
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The notion of (circular) colorings of edgeweighted graphs is introduced. This notion generalizes the notion of (circular) colorings of graphs, the channel assignment problem, and several other optimization problems. For instance, its restriction to colorings of weighted complete graphs corresponds
SemiSupervised Learning Using Gaussian Fields and Harmonic Functions
 IN ICML
, 2003
"... An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning ..."
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Cited by 748 (14 self)
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An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning
A distributed algorithm for minimumweight spanning trees
, 1983
"... A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
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Cited by 435 (3 self)
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A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm
On the complexity of vertexcoloring edgeweightings
 DISCRETE MATH. THEOR. COMPUT. SCI
, 2011
"... Given a graph G = (V,E) and a weight function w: E → R, a coloring of vertices of G, induced by w, is defined by χw(v) = e3v w(e) for all v ∈ V. In this paper, we show that determining whether a particular graph has a weighting of the edges from {1, 2} that induces a proper vertex coloring is NPcom ..."
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Cited by 8 (1 self)
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Given a graph G = (V,E) and a weight function w: E → R, a coloring of vertices of G, induced by w, is defined by χw(v) = e3v w(e) for all v ∈ V. In this paper, we show that determining whether a particular graph has a weighting of the edges from {1, 2} that induces a proper vertex coloring is NPcomplete.
Optimal Layout of EdgeWeighted Forests
, 1998
"... The layout problem for trees with weighted edges is motivated by the design of very large scale integrated circuits. Some of the nodes are fixed and the object is to position the remainder so that the total weighted edge cost is minimized. The cost of each edge is the product of its weight and its l ..."
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The layout problem for trees with weighted edges is motivated by the design of very large scale integrated circuits. Some of the nodes are fixed and the object is to position the remainder so that the total weighted edge cost is minimized. The cost of each edge is the product of its weight and its
LINEAR SYSTEMS ON EDGEWEIGHTED GRAPHS
"... Abstract. Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are Rvalued functions on the set of vertices and graph edges are permitted to have nonnegative weights in R. Using this generalization, we provide an independent proof of a RiemannRo ..."
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Abstract. Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are Rvalued functions on the set of vertices and graph edges are permitted to have nonnegative weights in R. Using this generalization, we provide an independent proof of a Riemann
Explorations of edgeweighted Cayley graphs . . .
, 2014
"... Let f: GF (p)n → GF (p). When p = 2, Bernasconi et al have shown that there is a correspondence between certain properties of f (eg, if it is bent) and properties of its associated Cayley graph. Analogously, but much earlier, Dillon showed that f is bent if and only if the “level curves ” of f had c ..."
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certain combinatorial properties (again, only when p = 2). The attempt is to investigate an analogous theory when p> 2 using the (apparently new) combinatorial concept of a weighted partial difference set. More precisely, we try to investigate which graphtheoretical properties of Γf can
Deterministic edgeweights in increasing tree families.
, 2008
"... In this work we study edge weights for two specific families of increasing trees, which include binary increasing trees and plane oriented recursive trees as special instances, where planeoriented recursive trees serve as a combinatorial model of scalefree random trees given by the m = 1 case of t ..."
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In this work we study edge weights for two specific families of increasing trees, which include binary increasing trees and plane oriented recursive trees as special instances, where planeoriented recursive trees serve as a combinatorial model of scalefree random trees given by the m = 1 case
Results 1  10
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567,914