Lower connectivities of regular graphs with small diameter☆

2007 ◽  
Vol 307 (11-12) ◽  
pp. 1255-1265
Author(s):  
C BALBUENA
Keyword(s):  
Small Diameter ◽  
Regular Graphs

CONNECTIVITY PROPERTIES IN RANDOM REGULAR GRAPHS WITH EDGE FAULTS

2000 ◽  
Vol 11 (02) ◽  
pp. 247-262 ◽  
Author(s):  
S. NIKOLETSEAS ◽  
K. PALEM ◽  
P. SPIRAKIS ◽  
M. YUNG
Keyword(s):  
Communication Network ◽  
Random Graphs ◽  
High Probability ◽  
Small Diameter ◽  
Regular Graphs ◽  
Connected Component ◽  
New Model

We introduce a new model of random graphs, that of random regular graphs with edge faults (which we denote by [Formula: see text]), obtained by selecting the edges of a random member of the set of all regular graphs of degree r independently and with probability p. We can thus represent a communication network in which the links fail independently and with probability f =1-p. In order to deal with this new model, we extend the notion of configurations and the translation lemma between configurations and random regular graphs provided by B. Bollobás, by introducing the concept of random configurations, to account for edge faults, and by providing an extended translation lemma between random configurations and [Formula: see text] graphs. We investigate important connectivity properties of [Formula: see text] by estimating the ranges of r, f for which, with high probability, [Formula: see text] graphs a) are highly connected b) become disconnected and c) admit a giant connected component of small diameter.

scholarly journals Lower connectivities of regular graphs with small diameter

2007 ◽  
Vol 307 (11-12) ◽  
pp. 1255-1265 ◽  
Author(s):  
C. Balbuena ◽  
X. Marcote
Keyword(s):  
Small Diameter ◽  
Regular Graphs

scholarly journals Number Theoretic Designs for Directed Regular Graphs of Small Diameter

2004 ◽  
Vol 17 (3) ◽  
pp. 377-383
Author(s):  
William D. Banks ◽  
Alessandro Conflitti ◽  
Igor E. Shparlinski
Keyword(s):  
Small Diameter ◽  
Regular Graphs

scholarly journals Pegging Graphs Yields a Small Diameter

2010 ◽  
Vol 20 (2) ◽  
pp. 239-248
Author(s):  
STEFANIE GERKE ◽  
ANGELIKA STEGER ◽  
NICHOLAS WORMALD
Keyword(s):  
Small Diameter ◽  
Peer To Peer ◽  
Regular Graphs ◽  
Cubic Graphs ◽  
Peer Network ◽  
Peer To Peer Network

We consider the following process for generating large random cubic graphs. Starting with a given graph, repeatedly add edges that join the midpoints of two randomly chosen edges. We show that the growing graph asymptotically almost surely has logarithmic diameter. This process is motivated by a particular type of peer-to-peer network. Our method extends to similar processes that generate regular graphs of higher degree.

scholarly journals The matching polynomial of a distance-regular graph

2000 ◽  
Vol 23 (2) ◽  
pp. 89-97 ◽  
Author(s):  
Robert A. Beezer ◽  
E. J. Farrell
Keyword(s):  
Regular Graph ◽  
Small Diameter ◽  
Intersection Array ◽  
Regular Graphs ◽  
Distance Regular Graph ◽  
Intersection Numbers ◽  
Matching Polynomial ◽  
Distance Regular Graphs

A distance-regular graph of diameterdhas2dintersection numbers that determine many properties of graph (e.g., its spectrum). We show that the first six coefficients of the matching polynomial of a distance-regular graph can also be determined from its intersection array, and that this is the maximum number of coefficients so determined. Also, the converse is true for distance-regular graphs of small diameter—that is, the intersection array of a distance-regular graph of diameter 3 or less can be determined from the matching polynomial of the graph.

scholarly journals Superconnectivity of regular graphs with small diameter

2009 ◽  
Vol 157 (7) ◽  
pp. 1349-1353 ◽  
Author(s):  
Camino Balbuena ◽  
Jianmin Tang ◽  
Kim Marshall ◽  
Yuqing Lin
Keyword(s):  
Small Diameter ◽  
Regular Graphs

A Replica Technique for the Inside Surfaces of Small Diameter Pipes and Tubes

1967 ◽  
Vol 25 ◽  
pp. 352-353
Author(s):  
T. G. Gregory
Keyword(s):  
Polyvinyl Chloride ◽  
Small Diameter ◽  
Replica Technique ◽  
Tube Size ◽  
Inside Diameter ◽  
Complete Inspection ◽  
Operating Limits

A nondestructive replica technique permitting complete inspection of bore surfaces having an inside diameter from 0.050 inch to 0.500 inch is described. Replicas are thermally formed on the outside surface of plastic tubing inflated in the bore of the sample being studied. This technique provides a new medium for inspection of bores that are too small or otherwise beyond the operating limits of conventional inspection methods.Bore replicas may be prepared by sliding a length of plastic tubing completely through the bore to be studied as shown in Figure 1. Polyvinyl chloride tubing suitable for this replica process is commercially available in sizes from 0.037- to 0.500-inch diameter. A tube size slightly smaller than the bore to be replicated should be used to facilitate insertion of the plastic replica blank into the bore.

Structural Organization and Distribution of Fiber Types in Extraocular Muscles of Cats

1972 ◽  
Vol 30 ◽  
pp. 34-35
Author(s):  
Asish C. Nag ◽  
Lee D. Peachey
Keyword(s):  
Fiber Type ◽  
Light And Electron Microscopy ◽  
Small Diameter ◽  
Extraocular Muscles ◽  
Fiber Types ◽  
Distinctive Features ◽  
Superior Rectus ◽  
Adult Cats ◽  
Different Diameters ◽  
Orbital Region

Cat extraocular muscles consist of two regions: orbital, and global. The orbital region contains predominantly small diameter fibers, while the global region contains a variety of fibers of different diameters. The differences in ultrastructural features among these muscle fibers indicate that the extraocular muscles of cats contain at least five structurally distinguishable types of fibers.Superior rectus muscles were studied by light and electron microscopy, mapping the distribution of each fiber type with its distinctive features. A mixture of 4% paraformaldehyde and 4% glutaraldehyde was perfused through the carotid arteries of anesthetized adult cats and applied locally to exposed superior rectus muscles during the perfusion.

Prospects for convergent beam electron diffraction with a 200kV cold field-emission transmission electron microscope

1991 ◽  
Vol 49 ◽  
pp. 466-467
Author(s):  
J W Steeds ◽  
R Vincent
Keyword(s):  
Field Emission ◽  
High Performance ◽  
Small Diameter ◽  
Convergent Beam Electron Diffraction ◽  
Zone Axis ◽  
Medium Voltage ◽  
Transmission Electron ◽  
Good Crystallinity ◽  
Special Modification ◽  
Convergent Beam

We review the analytical powers which will become more widely available as medium voltage (200-300kV) TEMs with facilities for CBED on a nanometre scale come onto the market. Of course, high performance cold field emission STEMs have now been in operation for about twenty years, but it is only in relatively few laboratories that special modification has permitted the performance of CBED experiments. Most notable amongst these pioneering projects is the work in Arizona by Cowley and Spence and, more recently, that in Cambridge by Rodenburg and McMullan.There are a large number of potential advantages of a high intensity, small diameter, focussed probe. We discuss first the advantages for probes larger than the projected unit cell of the crystal under investigation. In this situation we are able to perform CBED on local regions of good crystallinity. Zone axis patterns often contain information which is very sensitive to thickness changes as small as 5nm. In conventional CBED, with a lOnm source, it is very likely that the information will be degraded by thickness averaging within the illuminated area.

Applications of SIMS to electronic materials and devices

1992 ◽  
Vol 50 (2) ◽  
pp. 1682-1683
Author(s):  
S.F. Corcoran
Keyword(s):  
Depth Distribution ◽  
Secondary Ion Mass Spectrometry ◽  
Semiconductor Device ◽  
Electronic Materials ◽  
Profile Analysis ◽  
Semiconductor Industry ◽  
Small Diameter ◽  
Depth Resolution ◽  
Detection Sensitivity

Over the past decade secondary ion mass spectrometry (SIMS) has played an increasingly important role in the characterization of electronic materials and devices. The ability of SIMS to provide part per million detection sensitivity for most elements while maintaining excellent depth resolution has made this technique indispensable in the semiconductor industry. Today SIMS is used extensively in the characterization of dopant profiles, thin film analysis, and trace analysis in bulk materials. The SIMS technique also lends itself to 2-D and 3-D imaging via either the use of stigmatic ion optics or small diameter primary beams.By far the most common application of SIMS is the determination of the depth distribution of dopants (B, As, P) intentionally introduced into semiconductor materials via ion implantation or epitaxial growth. Such measurements are critical since the dopant concentration and depth distribution can seriously affect the performance of a semiconductor device. In a typical depth profile analysis, keV ion sputtering is used to remove successive layers the sample.

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