scholarly journals Comparing energy and Randic energy

2013 ◽  
Vol 32 (1) ◽  
pp. 117 ◽  
Author(s):  
Boris Furtula ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Connected Graph ◽  
Fixed Number ◽  
Molecular Graphs ◽  
Average Value ◽  
Underlying Graph

The recently conceived Randić energy (RE) is examined, and its relation to the (earlier much studied) total π-electron energy (E) is investigated. Within classes of molecular graphs, there exists a relatively good (increasing) linear correlation between RE and E. However, several significant differences between the structure-dependencies of RE and E have been discovered, the most striking of which is their dependence on the number m of edges of the underlying graph. Whereas, with increasing m, the average value of E increases, reaches a maximum and then decreases, the average value of RE monotonically decreases. The structure of the connected graph with a fixed number of vertices and maximal RE value was established.

On Statistics of Graph Energy

2001 ◽  
Vol 56 (3-4) ◽  
pp. 307-311 ◽  
Author(s):  
Ante Graovac ◽  
Ivan Gutman ◽  
Peter E. John ◽  
Dušica Vidović ◽  
Ivana Vlah
Keyword(s):  
Electron Energy ◽  
Molecular Graph ◽  
Molecular Graphs ◽  
Average Value ◽  
Graph Energy ◽  
The Absolute ◽  
The Difference ◽  
Conjugated Molecule

Abstract The energy EG of a graph G is the sum of the absolute values of the eigenvalues of G. In the case whene G is a molecular graph, EG is closely related to the total π-electron energy of the corresponding conjugated molecule. We determine the average value of the difference between the energy of two graphs, randomly chosen from the set of all graphs with n vertices and m edges. This result provides a criterion for deciding when two (molecular) graphs are almost coeneigetic.

scholarly journals Total π-electron energy and Laplacian energy: How far the analogy goes?

2007 ◽  
Vol 72 (12) ◽  
pp. 1343-1350 ◽  
Author(s):  
Slavko Radenkovic ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Molecular Graph ◽  
Total Electron ◽  
Good Linear ◽  
Molecular Graphs ◽  
Acyclic Graphs ◽  
Laplacian Energy ◽  
Total Electron Energy ◽  
Good Linear Correlation

The Laplacian energy LE is a newly introduced molecular-graph-based analog of the total ?-electron energy E. It is shown that LE and E have a similar structure-dependency only when molecules of different sizes are compared, when a good linear correlation between them exists. Within classes of isomers, LE and E are either not correlated at all or (as in the case of acyclic systems) are inversely proportional. The acyclic graphs and molecular graphs having the greatest and smallest LE values (determined in this work) differ significantly from those (previously known) having the greatest and smallest E values.

ON MOSTAR INDEX OF GRAPHS

2021 ◽  
Vol 10 (4) ◽  
pp. 2115-2129
Author(s):  
P. Kandan ◽  
S. Subramanian
Keyword(s):  
Connected Graph ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Topological Indices ◽  
Great Success ◽  
Complete Graphs ◽  
Molecular Graphs ◽  
Graphs And Networks ◽  
Complete Bipartite Graphs ◽  
Simple Connected Graph

On the great success of bond-additive topological indices like Szeged, Padmakar-Ivan, Zagreb, and irregularity measures, yet another index, the Mostar index, has been introduced recently as a peripherality measure in molecular graphs and networks. For a connected graph G, the Mostar index is defined as $$M_{o}(G)=\displaystyle{\sum\limits_{e=gh\epsilon E(G)}}C(gh),$$ where $C(gh) \,=\,\left|n_{g}(e)-n_{h}(e)\right|$ be the contribution of edge $uv$ and $n_{g}(e)$ denotes the number of vertices of $G$ lying closer to vertex $g$ than to vertex $h$ ($n_{h}(e)$ define similarly). In this paper, we prove a general form of the results obtained by $Do\check{s}li\acute{c}$ et al.\cite{18} for compute the Mostar index to the Cartesian product of two simple connected graph. Using this result, we have derived the Cartesian product of paths, cycles, complete bipartite graphs, complete graphs and to some molecular graphs.

Assessment of radioactivity from selected soil samples from Halfa Aljadida area, Sudan

2019 ◽  
Vol 107 (6) ◽  
pp. 489-502
Author(s):  
Abd-Elmoniem A. Elzain ◽  
Hajo Idriss ◽  
Yousif Sh. Mohammed ◽  
Khidir Shaib Mohamed ◽  
Mohamed Abd Elwahab Mohamed Ali ◽  
...  
Keyword(s):  
Effective Dose ◽  
Dose Rate ◽  
Linear Correlation ◽  
Radon Concentration ◽  
Soil Samples ◽  
Average Value ◽  
Soil Gas Radon ◽  
Effective Dose Rate ◽  
Alpha Index ◽  
Concentration Surface

Abstract In this research, the results of radon concentration, surface and mass exhalation rates, radium concentration, effective dose rate and the alpha index have been investigated in a number of 198 soil samples that have been collected from various residential locations of Halfa Aljadida area, Sudan. The can technique, containing CR-39 have been used. From our results, the average value of soil gas radon concentration was found to be 1.96±0.22 kBq·m−3. The average values of surface and mass exhalation rates were 1.73±0.19 Bq·m−2·h−1 and 34.79±3.87 mBq·kg−1·h−1, respectively. The radium concentration average value was 8.06±0.90 Bq·kg−1. While the average value of the effective dose rate was recorded to be 54.69±6.11 mSv·y−1. The average value of alpha index of studied samples was (4.03±0.45)×10−2. From the study, a good positive and linear correlation between radium concentration, surface and mass exhalation rates of soil samples were present. In addition to that, a positive and linear correlation between radium and radon concentrations was found. Finally, a comparison between the results and other findings was conducted and the results imply the fact that the area under consideration is safe as if the health hazard are mentioned.

Graham’s pebbling conjecture holds for the product of a graph and a sufficiently large complete bipartite graph

2019 ◽  
Vol 11 (06) ◽  
pp. 1950068
Author(s):  
Nopparat Pleanmani
Keyword(s):  
Bipartite Graph ◽  
Network Optimization ◽  
Connected Graph ◽  
Complete Bipartite Graph ◽  
Fixed Number ◽  
Arbitrary Vertex ◽  
Graph Pebbling ◽  
Vertex Set ◽  
Graham’S Conjecture ◽  
Pebbling Number

A graph pebbling is a network optimization model for the transmission of consumable resources. A pebbling move on a connected graph [Formula: see text] is the process of removing two pebbles from a vertex and placing one of them on an adjacent vertex after configuration of a fixed number of pebbles on the vertex set of [Formula: see text]. The pebbling number of [Formula: see text], denoted by [Formula: see text], is defined to be the least number of pebbles to guarantee that for any configuration of pebbles on [Formula: see text] and arbitrary vertex [Formula: see text], there is a sequence of pebbling movement that places at least one pebble on [Formula: see text]. For connected graphs [Formula: see text] and [Formula: see text], Graham’s conjecture asserted that [Formula: see text]. In this paper, we show that such conjecture holds when [Formula: see text] is a complete bipartite graph with sufficiently large order in terms of [Formula: see text] and the order of [Formula: see text].

Influence of the carbon/nitrogen relationship on the degree of autolysis of Aspergillus niger

1978 ◽  
Vol 56 (15) ◽  
pp. 1806-1808 ◽  
Author(s):  
R. Lahoz ◽  
Fuensanta Reyes ◽  
Pilar Gómez ◽  
Luis Jimeno
Keyword(s):  
Aspergillus Niger ◽  
Linear Correlation ◽  
Culture Medium ◽  
Regression Line ◽  
Average Value ◽  
Carbon Nitrogen Ratio ◽  
Nitrogen Ratio

The effect of the initial exogenous carbon/nitrogen ratio on the degree of autolysis in cultures of Aspergillus niger has been studied. For C/N ratios between 0.75:1 and 100:1 (grams per gram), the degree of autolysis (α) continuously decreased from an average value of 72.5 to 16.0%, respectively. There was a linear correlation between the [Formula: see text] ratio and the percentage degree of autolysis (α%) represented by the regression line [Formula: see text]. It can be concluded that the degree of autolysis is profoundly influenced by the C/N ratio initially present in the culture medium.

scholarly journals Edge Mostar Indices of Cacti Graph With Fixed Cycles

2021 ◽  
Vol 9 ◽  
Author(s):  
Farhana Yasmeen ◽  
Shehnaz Akhter ◽  
Kashif Ali ◽  
Syed Tahir Raza Rizvi
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Thermodynamic Characteristics ◽  
Chemical Compounds ◽  
Fixed Number ◽  
Common Vertex ◽  
Topological Invariants ◽  
Cactus Graph ◽  
Number Of Cycles

Topological invariants are the significant invariants that are used to study the physicochemical and thermodynamic characteristics of chemical compounds. Recently, a new bond additive invariant named the Mostar invariant has been introduced. For any connected graph ℋ, the edge Mostar invariant is described as Moe(ℋ)=∑gx∈E(ℋ)|mℋ(g)−mℋ(x)|, where mℋ(g)(or mℋ(x)) is the number of edges of ℋ lying closer to vertex g (or x) than to vertex x (or g). A graph having at most one common vertex between any two cycles is called a cactus graph. In this study, we compute the greatest edge Mostar invariant for cacti graphs with a fixed number of cycles and n vertices. Moreover, we calculate the sharp upper bound of the edge Mostar invariant for cacti graphs in ℭ(n,s), where s is the number of cycles.

scholarly journals New Results on the Forgotten Topological Index and Coindex

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Akbar Jahanbani ◽  
Maryam Atapour ◽  
Rana Khoeilar
Keyword(s):  
Electron Energy ◽  
Connected Graph ◽  
Topological Index ◽  
Nonadjacent Vertex ◽  
Zagreb Indices ◽  
Vertex Degrees ◽  
Simple Connected Graph

The ℱ -coindex (forgotten topological coindex) for a simple connected graph G is defined as the sum of the terms ζ G 2 y + ζ G 2 x over all nonadjacent vertex pairs x , y of G , where ζ G y and ζ G x are the degrees of the vertices y and x in G , respectively. The ℱ -index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972 in the same paper where the first and second Zagreb indices were introduced to study the structure dependency of total π -electron energy. Therefore, considering the importance of the ℱ -index and ℱ -coindex, in this paper, we study these indices, and we present new bounds for the ℱ -index and ℱ -coindex.

The effect of load application rate on the biomechanics of synthetic femurs

2009 ◽  
Vol 224 (4) ◽  
pp. 599-605 ◽  
Author(s):  
R Zdero ◽  
S Shah ◽  
M Mosli ◽  
E H Schemitsch
Keyword(s):  
Linear Correlation ◽  
Loading Rate ◽  
Application Rate ◽  
Torsional Stiffness ◽  
Fourth Generation ◽  
Axial Stiffness ◽  
Average Value ◽  
Rate Effects ◽  
Strong Linear Correlation ◽  
Torsional Test

Biomechanical investigations are increasingly using commercially available synthetic femurs as surrogates for human cadaveric femurs. However, the rate of force application in testing these artificial femurs appears to be chosen arbitrarily without much consideration to their visco-elastic time-dependent nature. The aim of this study, therefore, was to examine the effect of loading rate on the mechanical behaviour of synthetic femurs. Ten left, medium, fourth-generation composite femurs (Model 3403, Pacific Research Laboratories, Vashon, WA, USA) were fixed distally into cement-filled steel cubic chambers for mounting into a mechanical tester. In randomized order, each of the ten femurs was loaded at rates of 1, 2.5, 5, 7.5, 10, 20, 30, 40, 50, and 60 mm/min to obtain axial, lateral, and torsional stiffness. Axial stiffness showed an aggregate average value of 1742.7 ± 174.7 N/mm with a high linear correlation with loading rate ( R2 = 0.80). Lateral stiffness yielded an aggregate average value of 56.9 ± 10.2 N/mm and was linearly correlated with loading rate ( R2 = 0.85). Torsional stiffness demonstrated an aggregate average value of 176.9 ± 14.5 N/mm with a strong linear correlation with loading rate ( R2 = 0.59). Despite the high correlations between stiffness and speed, practically this resulted in an overall average difference between the lowest and highest stiffness of only 4 per cent. Moreover, no statistical comparisons between loading rates for axial, lateral, or torsional test modes showed differences ( p ≤ 0.843). Future biomechanical investigators utilizing these synthetic femurs need not be concerned with loading rate effects over the range tested presently. This is the first study in the literature to perform such an assessment.

Research on wind field characteristics measured in inland city by Lidar

2021 ◽  
Author(s):  
LI Jiawu ◽  
Jun WANG ◽  
WANG Feng
Keyword(s):  
Wind Speed ◽  
Probability Density ◽  
Density Function ◽  
Linear Correlation ◽  
Wind Direction ◽  
Measurement Data ◽  
Attack Angle ◽  
Average Value ◽  
Original Measurement ◽  
Positive Linear Correlation

Abstract In order to study the wind characteristics in inland cities, a Wind3D 6000 Lidar which has many advantages in measuring wind parameters was placed on a campus in Xi’an city. Then, through filtering the original measurement data, the wind speed, wind direction, wind attack angle and turbulence intensity were analyzed using the data of nearly four months ranging from 64m to 610m. It is found that during the field measurement period, there is a linear correlation and Lorentz density function distribution between wind speed and height, but the power index law is not obvious. The wind direction changes obviously with the time and season but less along the height. The probability density of wind attack angle presents Gauss distribution, with an average value of about 1.35°, which is negatively linear correlated with height and wind speed. The probability density of turbulence shows the distribution characteristic of LogNormal density function, which increases first and then decreases with the height, and has a positive linear correlation with the wind attack angle.

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