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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
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  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
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
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
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
., 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
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. ...
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
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
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
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>. ...
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
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
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
Lecture Notes in Computer Science
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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