scholarly journals The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1034 ◽  
Author(s):  
Weijun Liu ◽  
Jingwen Ban ◽  
Lihua Feng ◽  
Tao Cheng ◽  
Frank Emmert-Streib ◽  
...  
Keyword(s):  
Small Diameter ◽  
Hosoya Index ◽  
Unicyclic Graphs

The Hosoya index of a graph is defined by the total number of the matchings of the graph. In this paper, we determine the maximum Hosoya index of unicyclic graphs with n vertices and diameter 3 or 4. Our results somewhat answer a question proposed by Wagner and Gutman in 2010 for unicyclic graphs with small diameter.

scholarly journals On the Hosoya Indices of Bicyclic Graphs with Small Diameter

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Tingzeng Wu ◽  
Yong Yu
Keyword(s):  
Small Diameter ◽  
Sharp Bound ◽  
Hosoya Index ◽  
Np Complete ◽  
Bicyclic Graphs

Let G be a graph. The Hosoya index of G , denoted by z G , is defined as the total number of its matchings. The computation of z G is NP-Complete. Wagner and Gutman pointed out that it is difficult to obtain results of the maximum Hosoya index among tree-like graphs with given diameter. In this paper, we focus on the problem, and a sharp bound of Hosoya indices of all bicyclic graphs with diameter of 3 is determined.

scholarly journals Erratum: Liu, W.; Ban, J.; Feng, L.; Cheng, T.; Emmert-Streib, F.; Dehmer, M. The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four. Symmetry 2019, 11, 1034

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1496
Author(s):  
Weijun Liu ◽  
Jingwen Ban ◽  
Lihua Feng ◽  
Tao Cheng ◽  
Frank Emmert-Streib ◽  
...  
Keyword(s):  
Hosoya Index ◽  
Unicyclic Graphs

The authors wish to make the following corrections to their paper [...]

scholarly journals The largest n - 1 Hosoya indices of unicyclic graphs

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2573-2581 ◽  
Author(s):  
Guihai Yu ◽  
Lihua Feng ◽  
Aleksandar Ilic
Keyword(s):  
Independent Sets ◽  
Hosoya Index ◽  
Unicyclic Graphs ◽  
Molecular Graphs ◽  
Appl Math

The Hosoya index Z(G) of a graph G is defined as the total number of edge independent sets of G. In this paper, we extend the research of [J. Ou, On extremal unicyclic molecular graphs with maximal Hosoya index, Discrete Appl. Math. 157 (2009) 391-397.] and [Y. Ye, X. Pan, H. Liu, Ordering unicyclic graphs with respect to Hosoya indices and Merrifield-Simmons indices, MATCH Commun. Math. Comput. Chem. 59 (2008) 191-202.] and order the largest n - 1 unicyclic graphs with respect to the Hosoya index.

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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