Total eccentricity index of trees with fixed pendent vertices and trees with fixed diameter

2021 ◽  
Author(s):  
Rashid Farooq ◽  
Shehnaz Akhter ◽  
Juan Rada
Keyword(s):  
Eccentricity Index ◽  
Pendent Vertices

On the largest matching roots of graphs with a given number of pendent vertices

2019 ◽  
Vol 255 ◽  
pp. 339-344
Author(s):  
Hailiang Zhang ◽  
Guangting Chen ◽  
Guanglong Yu
Keyword(s):  
Pendent Vertices

On the maximum connective eccentricity index among k-connected graphs

2020 ◽  
pp. 2150002
Author(s):  
Fazal Hayat
Keyword(s):  
Minimum Degree ◽  
Independence Number ◽  
Connected Graphs ◽  
Eccentricity Index

The connective eccentricity index (CEI for short) of a graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the degree of [Formula: see text] and [Formula: see text] is the eccentricity of [Formula: see text] in [Formula: see text]. In this paper, we characterize the unique graphs with maximum CEI from three classes of graphs: the [Formula: see text]-vertex graphs with fixed connectivity and diameter, the [Formula: see text]-vertex graphs with fixed connectivity and independence number, and the [Formula: see text]-vertex graphs with fixed connectivity and minimum degree.

scholarly journals Algebraic connectivity for subclasses of caterpillars

2010 ◽  
Vol 4 (1) ◽  
pp. 181-196 ◽  
Author(s):  
Nair Abreu ◽  
Oscar Rojo ◽  
Claudia Justel
Keyword(s):  
The Other ◽  
Algebraic Connectivity ◽  
Pendent Vertices

A caterpillar is a tree in which the removal of all pendent vertices make it a path. In this paper, we consider two classes of caterpillars. We present an ordering of caterpillars by algebraic connectivity in one of them and find one that maximizes the algebraic connectivity in the other class.

scholarly journals The spectral radius of tricyclic graphs with n vertices and k pendent vertices

2008 ◽  
Vol 428 (11-12) ◽  
pp. 2639-2653 ◽  
Author(s):  
Xianya Geng ◽  
Shuchao Li
Keyword(s):  
Spectral Radius ◽  
Tricyclic Graphs ◽  
Pendent Vertices

The extremal values of connective eccentricity index for trees and unicyclic graphs

2016 ◽  
Vol 94 (3) ◽  
pp. 437-453 ◽  
Author(s):  
Lang Tang ◽  
Xia Wang ◽  
Weijun Liu ◽  
Lihua Feng
Keyword(s):  
Unicyclic Graphs ◽  
Eccentricity Index ◽  
Extremal Values

scholarly journals Effect of interventional edge-to-edge repair in tricuspid regurgitation on ring dimensions

2021 ◽  
Vol 42 (Supplement_1) ◽  
Author(s):  
B Goebel ◽  
C Salomon ◽  
M Abdulrahman ◽  
S Richter ◽  
M El Garhy ◽  
...  
Keyword(s):  
Tricuspid Valve ◽  
Right Atrial ◽  
Area Change ◽  
Vena Contracta ◽  
Eccentricity Index ◽  
Ring Shape ◽  
Maximal Diameter ◽  
Reduced Ring ◽  
The Impact ◽  
Full Volume

Abstract Background The concept of percutaneous tricuspid valve edge-to-edge repair (pTVR) is based on the connection of leaflets in the area of insufficiency using a coaptation device. By closing the coaptation device a considerable tractive force is applied on the leaflets, which might have an effect on the valve ring. Aim of the study was to examine the impact of device implantation on tricuspid ring dimensions. Methods During pTVR 3D zoom loops of tricuspid valve were acquired before and after clip placement using transoesophageal echocardiography. Measurements of TV ring dimensions included the following parameters: ring area (TV area), maximal diameter, minimal diameter, eccentricity index (Figure 1). Tenting area was derived from a four-chamber view of the valve. In addition, regurgitation severity was graded from 1+ to 5+ by measuring vena contracta area (VCA3D) in 3D full volume colour Doppler loop using multiplanar reconstruction. Right atrial (RA) and ventricular volumes (RVVd3D, RVVs3D) and function (RVEF3D) were assessed in a 3D full volume loop. Results The study population comprised 97 patients (age 78±6 years, 47 male), who underwent pTVR at our hospital. As expected cavity dimension correlated with TV area size (for RVVd3D r=0.51, p<0.001 and for RA volume r=0.71, p<0.001). The mean TV ring area was significantly reduced (ring area 8.53±2.23 cm2/m2BSA vs. 7.55±2.18 cm2/m2BSA, p<0.001) and the ring shape became more oval (Eccentricity index 1.2±0.15 vs. 1.29±0.17, p<0.001) after pTVR. The reduction of ring area (12±7%, range 0.7–28%) showed an only modest correlation to the number of implanted coaptation devices (r=0.30, p<0.001) and percentage reduction of VCA3D (r=0.36, p<0.001). In the patient group with a ring area change ≥12% a reduction to TR grade ≤2+ by pTVR was achieved in 83% of cases, whereas only 62% of patients reached moderate TR when area change was below 12%. Conclusion pTVR using coaptation devices reduces the ring area. This effect is related to the number of devices implanted. FUNDunding Acknowledgement Type of funding sources: None.

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