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On Optimal Edge Numberings of the nCube Graph
 DISCRETE APPL. MATH
, 1993
"... Given two disjoint groups U and V each containing 2 n−1 people. Suppose an experiment (or a game) requires pairwise comparisons between u ∈ U and v ∈ V in such a way that u ∈ U (v ∈ V) is compared exactly with n people v ∈ V (u ∈ U). Only one comparison can be done at a time, and the comparisons are ..."
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Cited by 2 (1 self)
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are made along the n2 n−1 edges of the n−cube graph Qn with vertex classes U and V. The paper deals with sequential orderings of these n2 n−1 pairs (u, v) ∈ U ×V for which the maximum time duration a person has to stay in the sequence for comparison purposes or the total time duration of the 2 n people
Performance analysis of kary ncube interconnection networks
 IEEE Transactions on Computers
, 1990
"... AbstmctVLSI communication networks are wirelimited. The cost of a network is not a function of the number of switches required, but rather a function of the wiring density required to construct the network. This paper analyzes communication networks of varying dimension under the assumption of co ..."
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Cited by 359 (18 self)
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of constant wire bisection. Expressions for the latency, average case throughput, and hotspot throughput of kary ncube networks with constant bisection are derived that agree closely with experimental measurements. It is shown that lowdimensional networks (e.g., tori) have lower latency and higher hot
Edge Detection
, 1985
"... For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the s ..."
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Cited by 1277 (1 self)
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about the physical properties of the scene are provided by the changes of intensity in the image. The importance of intensity changes and edges in early visual processg has led to extensive research on their detection, description and .use, both in computer and biological vision systems. This article
Forwardingindices of folded ncubes �
"... For a given connected graph G of order n, a routing R is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of a graph is the maximum number of paths of R passingthrough any vertex (resp. edge) in the graph. In this paper, t ..."
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For a given connected graph G of order n, a routing R is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of a graph is the maximum number of paths of R passingthrough any vertex (resp. edge) in the graph. In this paper
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Interval Edge Colourings of Complete Graphs and ncubes
, 2007
"... For complete graphs and ncubes bounds are found for the possible number of colours in an interval edge colourings. Let G = (V, E) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G) is den ..."
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Cited by 1 (1 self)
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For complete graphs and ncubes bounds are found for the possible number of colours in an interval edge colourings. Let G = (V, E) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G
EVOLUTION OF THE nCUBE
, 1979
"... Let C ” denote the graph with vertices @I,. . . ,e,,) , ei = 0,i and vertices adjacent if they differ in exactly one coordinate. We call C ” the ncube. Let G = G., denote the random subgraph of C ” defined by letting Prob(IijlEG)=p for ah & jE CR and letting these probabilities be mutually ..."
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Cited by 26 (1 self)
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Let C ” denote the graph with vertices @I,. . . ,e,,) , ei = 0,i and vertices adjacent if they differ in exactly one coordinate. We call C ” the ncube. Let G = G., denote the random subgraph of C ” defined by letting Prob(IijlEG)=p for ah & jE CR and letting these probabilities be mutually
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional
Results 1  10
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572,425