scholarly journals k-super cube root cube mean labeling of graphs

2021 ◽  
Vol 40 (5) ◽  
pp. 1097-1116
Author(s):  
V. Princy Kala
Keyword(s):  
Cube Root ◽  
Injective Function ◽  
Edge Labeling

Consider a graph G with |V (G)| = p and |E(G)| = q and let f : V (G) → {k, k + 1, k + 2, . . . p + q + k − 1}} be an injective function. The induced edge labeling f ∗ for a vertex labeling f is defined by f ∗ (e) =  for all e = uv ∈ E(G) is bijective. If f(V (G)) ∪ {f ∗ (e) : e ∈ E(G)} = {k, k + 1, k + 2, . . . , p + q + k − 1}, then f is called a k-super cube root cube mean labeling. If such labeling exists, then G is a k-super cube root cube mean graph. In this paper, I introduce k-super cube root cube mean labeling and prove the existence of this labeling to the graphs viz., triangular snake graph Tn, double triangular snake graph D(Tn), Quadrilateral snake graph Qn, double quadrilateral snake graph D(Qn), alternate triangular snake graph A(Tn), alternate double triangular snake graph AD(Tn), alternate quadrilateral snake graph A(Qn), & alternate double quadrilateral snake graph AD(Qn).

scholarly journals Super Lehmer-3 Mean Labeling

2016 ◽  
Vol 8 (5) ◽  
pp. 29
Author(s):  
S. Somasundaram ◽  
S. S. Sandhya ◽  
T. S. Pavithra
Keyword(s):  
Injective Function ◽  
Edge Labeling

Let f:V(G)-&gt;{1,2,.....p+q} be an injective function .The induced edge labeling f*(e=uv) is defined by ,f*(e)=[(f(u)^3+f(v)^3)/(f(u)^2+f(v)^2 )] (or) [(f(u)^3+f(v)^3)/(f(u)^2+f(v)^2 )], then f is called Super Lehmer-3 mean labeling, if {f (V(G))} U {f(e)/e ∈ E(G)}={1,2,3,.....p+q}, A graph which admits Super Lehmer-3 Mean labeling is called Super Lehmer-3 Mean graph.<br />In this paper we prove that Path, Comb, Ladder, Crown are Super Lehmer-3 mean graphs.

scholarly journals k-Zumkeller labeling of super subdivision of some graphs

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
M. Basher
Keyword(s):  
Simple Graph ◽  
Natural Numbers ◽  
Injective Function ◽  
Planar Grid ◽  
Circular Ladder

AbstractA simple graph $$G=(V,E)$$ G = ( V , E ) is said to be k-Zumkeller graph if there is an injective function f from the vertices of G to the natural numbers N such that when each edge $$xy\in E$$ x y ∈ E is assigned the label f(x)f(y), the resulting edge labels are k distinct Zumkeller numbers. In this paper, we show that the super subdivision of path, cycle, comb, ladder, crown, circular ladder, planar grid and prism are k-Zumkeller graphs.

scholarly journals A Reliability Based Model for Wind Turbine Selection

2013 ◽  
Vol 2 (2) ◽  
pp. 69-74 ◽  
Author(s):  
A.K. Rajeevan ◽  
P.V. Shouri ◽  
Usha Nair
Keyword(s):  
Power Generation ◽  
Wind Speed ◽  
Wind Turbine ◽  
Wind Power ◽  
Point Of View ◽  
Cube Root ◽  
Mathematical Relationship ◽  
Turbine Generator ◽  
Wind Turbine Generator ◽  
A Site

A wind turbine generator output at a specific site depends on many factors, particularly cut- in, rated and cut-out wind speed parameters. Hence power output varies from turbine to turbine. The objective of this paper is to develop a mathematical relationship between reliability and wind power generation. The analytical computation of monthly wind power is obtained from weibull statistical model using cubic mean cube root of wind speed. Reliability calculation is based on failure probability analysis. There are many different types of wind turbinescommercially available in the market. From reliability point of view, to get optimum reliability in power generation, it is desirable to select a wind turbine generator which is best suited for a site. The mathematical relationship developed in this paper can be used for site-matching turbine selection in reliability point of view.

Estimating the Parameters of a Cube Root Normal Distribution from Reduced Sample Data

1985 ◽  
Vol 21 (1) ◽  
pp. 89-90
Author(s):  
C. J. Potratz ◽  
R. K. Steinhorst ◽  
C. L. Hanson
Keyword(s):  
Normal Distribution ◽  
Cube Root ◽  
Sample Data

scholarly journals Weak integer additive set-labeled graphs: A creative review

2015 ◽  
Vol 08 (03) ◽  
pp. 1550052 ◽  
Author(s):  
N. K. Sudev ◽  
K. A. Germina ◽  
K. P. Chithra
Keyword(s):  
Binary Operation ◽  
Labeled Graphs ◽  
Injective Function ◽  
Power Set

For a non-empty ground set [Formula: see text], finite or infinite, the set-valuation or set-labeling of a given graph [Formula: see text] is an injective function [Formula: see text], where [Formula: see text] is the power set of the set [Formula: see text]. A set-valuation or a set-labeling of a graph [Formula: see text] is an injective set-valued function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text] for every [Formula: see text], where [Formula: see text] is a binary operation on sets. Let [Formula: see text] be the set of all non-negative integers and [Formula: see text] be its power set. An integer additive set-labeling (IASL) is defined as an injective function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text]. An IASL [Formula: see text] is said to be an integer additive set-indexer if [Formula: see text] is also injective. A weak IASL is an IASL [Formula: see text] such that [Formula: see text]. In this paper, critical and creative review of certain studies made on the concepts and properties of weak integer additive set-valued graphs is intended.

Cage size and flight speed of the tobacco hawkmoth Manduca sexta

1995 ◽  
Vol 198 (8) ◽  
pp. 1665-1672 ◽  
Author(s):  
R Stevenson ◽  
K Corbo ◽  
L Baca ◽  
Q Le
Keyword(s):  
Manduca Sexta ◽  
Flight Speed ◽  
Flight Behavior ◽  
Cube Root ◽  
The Third ◽  
Chamber Volume ◽  
Cage Size ◽  
Allometric Analysis ◽  
Size Limits ◽  
Chamber Size

Flight speeds and behaviors of the sphinx moth Manduca sexta were recorded in chambers of four different sizes (0.57, 8.5, 44 and 447 m3). Mean horizontal speed increased linearly with the cube root of chamber volume from 0.57 m s-1 in the smallest chamber to 3.4 m s-1 in the largest. The maximum horizontal speed observed was 5.3 m s-1 in the largest chamber. Speeds decreased linearly with the logarithm of hawkmoth proximity to the wall. In a tunnel chamber (the third largest), moths often flew in a scalloped-shaped path. At the top of the scallop, they glided for 1&shy;5 wing beats. In the largest chamber, moths could be recorded flying at angles other than horizontal (0 &deg;). At flight angles greater or less than 0 &deg;, mean speed decreased linearly with angle until &plusmn;40 &deg;. At greater angles, speeds remained between 1 and 2 m s-1. Moths also flew closer to the wall at flight angles deviating from the horizontal. An allometric analysis of the flight speeds of insects and birds suggests that M. sexta may be able to fly at 7&shy;10 m s-1. We conclude that chamber size limits the flight speed and modifies the flight behavior of the tobacco hawkmoth.

Evidence for the homothetic scaling of urban forms

2018 ◽  
Vol 47 (5) ◽  
pp. 870-888 ◽  
Author(s):  
Rémi Lemoy ◽  
Geoffrey Caruso
Keyword(s):  
Land Use ◽  
Population Density ◽  
Scaling Laws ◽  
Radial Distance ◽  
Three Dimensions ◽  
City Size ◽  
Cube Root ◽  
Radial Profiles ◽  
Population Grid ◽  
Urban Scaling

The size and form of cities influence their social and environmental impacts. Whether cities have the same form irrespective of their size is still an open question. We analyse the profile of artificial land and population density, with respect to the distance to their main centre, for the 300 largest European cities. Our analysis combines the GMES/Copernicus Urban Atlas 2006 land use database at 5 m resolution for 300 larger urban zones with more than 100,000 inhabitants and the Geostat population grid at 1 km resolution. We find a remarkable constancy of radial profiles across city sizes. Artificial land profiles scale in the two horizontal dimensions with the square root of city population, while population density profiles scale in three dimensions with its cube root. In short, cities of different size are homothetic in terms of land use and population density, which challenges the idea that larger cities are more parsimonious in the use of land per capita. While earlier literature documented the scaling of average densities (total surface and population) with city size, we document the scaling of the whole radial distance profile with city size, thus liaising intra-urban radial analysis and systems of cities. Our findings also yield homogenous spatial definitions of cities, from which we can re-question urban scaling laws and Zipf’s law for cities.

Collagen and elastin fibers in human pulmonary alveolar walls

1988 ◽  
Vol 64 (4) ◽  
pp. 1659-1675 ◽  
Author(s):  
S. S. Sobin ◽  
Y. C. Fung ◽  
H. M. Tremer
Keyword(s):  
Transpulmonary Pressure ◽  
Collagen Fibers ◽  
Capillary Blood ◽  
Fiber Bundles ◽  
Cube Root ◽  
Inflation Pressure ◽  
Frequency Distributions ◽  
Normal Distributions ◽  
Statistical Frequency ◽  
The Mean

The morphology and morphometric data of collagen and elastin fibers in the pulmonary alveolar walls are presented. Specimens were obtained from postmortem lungs quick-frozen at specified transpulmonary pressures. Collagen was stained by silver, and elastin was stained by orcein. Photomicrographs were composed by computer. Young lungs typically show small collagen fibers that radiate from the "posts," whereas larger fiber bundles traverse the septum irrespective of capillary blood vessels. In older lungs, rings of collagen around the posts appear enlarged. Elastin bundles do not show obvious variation in pattern with age and inflation pressure. Statistical frequency distributions of the fiber width and curvature are both skewed, but the square root of the width and the cube root of the curvature have approximate normal distributions. Typically, for young lungs at transpulmonary pressure of 4 cmH2O, the mean of (width)1/2 (in micron1/2) for collagen fibers is 0.952 +/- 0.242 (SD), that of (curvature)1/3 (in micron-1/3) is 0.349 +/- 0.094. The corresponding values for elastin are 0.986 +/- 0.255 and 0.395 +/- 0.094.

scholarly journals On the Topology of the Cambrian Semilattices

10.37236/2910 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Myrto Kallipoliti ◽  
Henri Mühle
Keyword(s):  
Coxeter Group ◽  
Closed Interval ◽  
Open Interval ◽  
Weak Order ◽  
Edge Labeling

For an arbitrary Coxeter group $W$, Reading and Speyer defined Cambrian semilattices $\mathcal{C}_{\gamma}$ as sub-semilattices of the weak order on $W$ induced by so-called $\gamma$-sortable elements. In this article, we define an edge-labeling of $\mathcal{C}_{\gamma}$, and show that this is an EL-labeling for every closed interval of $\mathcal{C}_{\gamma}$. In addition, we use our labeling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Reading.

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