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Dense group networks
1992
Discrete Applied Mathematics
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Dense group networks. Discrete Applied Mathematics 37/38 (1992) 65-71. ...
Significant improvements have recently been made to many of the lower bounds for the largest graphs of given degree and diameter. ...
Campbell
Cayley graphs The graphs were constructed from finite linear groups, specifically the general linear groups CL(2,k) and the speciai linear groups SL (2,k) . ...
doi:10.1016/0166-218x(92)90125-t
fatcat:rfhlsrkwcjdj5hmn7jdtdmyzkm
Vertex-symmetric digraphs with small diameter
1995
Discrete Applied Mathematics
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There is increasing interest in the design of dense vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. ...
In this paper we give new families of dense vertex-symmetric (A, D) digraphs, that is large digraphs with a given maximum out-degree A and diameter at most D. ...
More recently, Dinneen [6] updated the table with constructions based on Cayley graphs from linear groups and semi-direct products of cyclic groups. ...
doi:10.1016/0166-218x(93)e0145-o
fatcat:bzitgheevnbq3iw2mglihypsim
On Cyclic Codes of Odd Lengths from the Stable Variety of Regular Cayley Graphs
2018
Mathematics and Statistics
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This paper concerns the utilization of the stable variety of Cayley regular graphs of odd order for efficient interconnection networks as studied, in the area of Codes Generation and Analysis. ...
Some small classes of linear and cyclic codes from the adjacency matrices of some Eulerian graphs due to the (132)/(123)-avoiding patterns of Audu and Aminu (AUNU) permutations [4, 5] . ...
Symmetric Matrix
Methodology
Formulation of the 2-Stable Degree/Diameter Network Model Here, we present a step by step procedure of the succession scheme for the construction of this variety of Cayley ...
doi:10.13189/ms.2018.060201
fatcat:mq2yfoxavfet3n367n7yekqdbe
Asymmetry of Retinal Arteriolar Branch Widths at Junctions Affects Ability of Formulae to Predict Trunk Arteriolar Widths
2006
Investigative Ophthalmology and Visual Science
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In the second group, the mean arteriolar trunk diameter was 15.56 pixels. ...
To describe a revised formula for the estimation of retinal trunk arteriole widths from their respective arteriolar branch widths that improves the summarizing of retinal arteriolar diameters. ...
The predictive ability of the regression model for the BC formed from the "training" group to determine the trunk diameter from the two branch vessel diameters was compared with the constant BC of Knudtson ...
doi:10.1167/iovs.05-1248
pmid:16565364
fatcat:yue6xrmilnfmzigktaymxwk3pu
Book announcements
1990
Discrete Applied Mathematics
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Euclidean space groups and
the torus. Triangle groups). Groups of small symmetric genus (The Riemann-Hurwitz
equation revisited.
Strong symmetric genus 0. Symmetric genus 1. ...
The geometry and algebra of groups of symmetric genus
1. Hurwitz's theorem). Groups of small genus (An example. A face-size inequality. Statement of main
theorem. ...
doi:10.1016/0166-218x(90)90074-m
fatcat:uhwd4fl3wvcetkvers2zklsbry
Periodically regular chordal rings
1999
IEEE Transactions on Parallel and Distributed Systems
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., from linear to logarithmic diameter), while maintaining an elegant framework for computation and communication. ...
In this paper, periodically regular chordal (PRC) ring networks are proposed as a compromise for combining low node degree with small diameter. ...
These networks combine the benefits of low node degree, small diameter, and a very simple routing framework. ...
doi:10.1109/71.774913
fatcat:6hyc53mngfehbchy5opccnrgqu
Page 3805 of Mathematical Reviews Vol. , Issue 95g
[page]
1995
Mathematical Reviews
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The network G ...
The lower bound follows from a case analysis of possible cores, combined with estimates for the dual of the linear programming problem. ...
A Structured Table of Graphs with Symmetries and Other Special Properties
2019
Symmetry
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These optimal graphs, many of which are newly discovered, may find wide applications, for example, in design of network topologies. ...
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. ...
general linear group obtained from GL(n, p) S n Symmetric group on a set of length n Aut ( Tables 2-4 . ...
doi:10.3390/sym12010002
fatcat:ysv4hahmhva6fivhqk76in6uxq
Large Cayley graphs on an abelian group
1997
Discrete Applied Mathematics
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In this paper we determine new bounds on the maximum number of vertices of a Cayley graph with fixed diameter and degree on an abelian group. ...
All Cayley graphs are vertex-transitive, and therefore correspond to "totally symmetric" networks. ...
However, not all graphs are convenient for interconnection network purposes, and additional properties may be required. For instance, routing is much easier if the network is highly symmetric. ...
doi:10.1016/s0166-218x(96)00084-4
fatcat:77kptnufznhbxfbqv5s2ceewhy
Does the Type of Event Influence How User Interactions Evolve on Twitter?
2015
PLoS ONE
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Interactions have been modeled as networks that are annotated with the time markers. We study changes in the structural properties at both the network level and the node level. ...
The number of people using on-line social networks as a new way of communication is continually increasing. ...
The evolution of the number of symmetric links, average diameter, average path, and clustering in conferences is different from the rest of events. ...
doi:10.1371/journal.pone.0124049
pmid:25961305
pmcid:PMC4427504
fatcat:3pd3epzomjby7k7rm6fnrv5a3y
Page 5534 of Mathematical Reviews Vol. , Issue 94i
[page]
1994
Mathematical Reviews
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Any time-invariant linear network can be analyzed. The network can involve any kind of pure or controlled sources. ...
Summary: “Chaos has been widely reported and studied in Chua’s circuit family, which is characterized by a 21-parameter family of odd-symmetric piecewise-linear vector fields in R>. ...
A local graph rewiring algorithm for sampling spanning trees
[article]
2017
arXiv
pre-print
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We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. ...
We prove that the algorithm is ergodic and proceed to estimate the probability distribution for small graph ensembles with exactly known probabilities. ...
This cluster was funded through grants from Science Foundation Ireland. ...
arXiv:1711.07432v1
fatcat:pgrzpjxdmvcsxgaeinihs5fnlq
Dermoscopic Evaluation of Amelanotic and Hypomelanotic Melanoma
2008
Archives of Dermatology
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Diagnostic models were derived from and tested on independent randomly selected lesions. Setting: Predominantly hospital-based clinics from 5 continents. ...
This 6ϫ 5-mm raised yellow lesion has small-diameter arborizing (thick arrows) and linear irregular vessels (thin arrows). ...
pigmentation pattern, blue-gray globules that were irregular in size and/or distribution, multiple blue-gray globules, arborizing small diameter vessels, and symmetrical shape. ...
doi:10.1001/archderm.144.9.1120
pmid:18794455
fatcat:ipwygv67hbcnza7laanlosuyka
Locality, Communication, and Interconnect Length in Multicomputers
1988
SIAM journal on computing (Print)
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An example of a network with small diameter which is not symmetric in this sense is the tree. ...
In fact, the arguments hold for networks with a small diameter which satisfy certain symmetry requirements. ...
doi:10.1137/0217042
fatcat:cll6m4t44nd5dasexa7zgpus2y
Mining Graphs with Constraints on Symmetry and Diameter
[chapter]
2010
Lecture Notes in Computer Science
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We propose a novel algorithm that finds subgraphs of limited diameter and high symmetry. These subgraphs represent the more structurally interesting patterns in the database. ...
real-world networks and find that, in contrast to classical random graph models, many real-world networks are richly symmetric". ...
The importance of mining symmetric graphs in social networks is discussed for example in [MSA1] , there they claim: "We consider the size and structure of the automorphism groups of a variety of empirical ...
doi:10.1007/978-3-642-16720-1_1
fatcat:sqa33jmf5rha7hlfiqogqddsym
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