scholarly journals On k-Distance Degree Index of Trees

2021 ◽  
Vol 10 (3) ◽  
pp. 1584-1588
Keyword(s):  
Connected Graph ◽  
Fixed Number ◽  
Minimum Index

Let G be a connected graph then ܰ௞-index (݇-distance degree index) defined in [14] as ܰ௞(ܩ)=∑ௗ௜௔௠(ீ)௞ୀଵቀ∑௫ఢ௏(ீ)݀௞(ݔ)ቁ݇, where ݀௞(ݔ)=|ܰ௞(ݔ)|=|{ݕܸ߳(ܩ):݀(ݔ,ݕ)=݇}|, where ݀(ݔ,ݕ)is the distance between vertex ݔand ݕin graph ܩand ݉ܽ݅݀(ܩ)is the diameter of graph ܩ. We define some transformations and their impact on ܰ௞-index of graphs with respect to pendant path and pendant vertices. For fixed number of pendant vertices of a tree, we define a tree with minimum ܰ௞-index. Also for different fixed parameters we characterize the tress with minimum ܰ௞-index.

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].

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 Minimum eccentric connectivity index for graphs with fixed order and fixed number of pendant vertices

2019 ◽  
Vol 29 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Gauvain Devillez ◽  
Alain Hertz ◽  
Hadrien Mélot ◽  
Pierre Hauweele
Keyword(s):  
Connected Graph ◽  
Fixed Number ◽  
Connectivity Index ◽  
Maximum Distance ◽  
Eccentric Connectivity Index ◽  
Connected Graphs ◽  
Fixed Order ◽  
Elegant Proof

The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G. We characterize, with a new elegant proof, those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order n. Then, given two integers n and p with p ? n - 1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pendant vertices.

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.

Interactive multiobjective DEA target setting using lexicographic DDF

2020 ◽  
Vol 54 (6) ◽  
pp. 1703-1722 ◽  
Author(s):  
Narges Soltani ◽  
Sebastián Lozano
Keyword(s):  
Efficient Frontier ◽  
Directional Distance Function ◽  
Fixed Number ◽  
Optimization Approach ◽  
Target Setting ◽  
Interactive Process ◽  
Decision Making Unit ◽  
Setting Approach ◽  
Promising Area ◽  
Current Region

In this paper, a new interactive multiobjective target setting approach based on lexicographic directional distance function (DDF) method is proposed. Lexicographic DDF computes efficient targets along a specified directional vector. The interactive multiobjective optimization approach consists in several iteration cycles in each of which the Decision Making Unit (DMU) is presented a fixed number of efficient targets computed corresponding to different directional vectors. If the DMU finds one of them promising, the directional vectors tried in the next iteration are generated close to the promising one, thus focusing the exploration of the efficient frontier on the promising area. In any iteration the DMU may choose to finish the exploration of the current region and restart the process to probe a new region. The interactive process ends when the DMU finds its most preferred solution (MPS).

Phospholipid-Protein Interactions in the Formation of Prothrombin Activator

1965 ◽  
Vol 14 (03/04) ◽  
pp. 431-444 ◽  
Author(s):  
E. R Cole ◽  
J. L Koppel ◽  
J. H Olwin
Keyword(s):  
Complex Formation ◽  
Protein Interactions ◽  
Calcium Ions ◽  
Fixed Number ◽  
Factor V ◽  
Clotting Factors ◽  
Number Of Binding Sites ◽  
C Complex ◽  
Autoprothrombin C

SummarySince Ac-globulin (factor V) is involved in the formation of prothrombin activator, its ability to complex with phospholipids was studied. Purified bovine Ac-globulin was complexed to asolectin, there being presumably a fixed number of binding sites on the phospholipid micelle for Ac-globulin. In contrast to the requirement for calcium ions in the formation of complexes between asolectin and autoprothrombin C, calcium ions were not required for complex formation between asolectin and Ac-globulin to occur ; in fact, the presence of calcium prevented complex formation occurring, the degree of inhibition being dependent on the calcium concentration. By treating isolated, pre-formed aso- lectin-Ac-globulin complexes with calcium chloride solutions, Ac-globulin could be recovered in a much higher state of purity and essentially free of asolectin.Complete activators were formed by first preparing the asolectin-calcium- autoprothrombin C complex and then reacting the complex with Ac-globulin. A small amount of this product was very effective as an activator of purified prothrombin without further addition of calcium or any other cofactor. If the autoprothrombin C preparation used to prepare the complex was free of traces of prothrombin, the complete activator was stable for several hours at room temperature. Stable preparations of the complete activator were centrifuged, resulting in the sedimentation of most of the activity. Experimental evidence also indicated that activator activity was highest when autoprothrombin C and Ac-globulin were complexed to the same phospholipid micelle, rather than when the two clotting factors were complexed to separate micelles. These data suggested that the in vivo prothrombin activator may be a sedimentable complex composed of a thromboplastic enzyme, calcium, Ac-globulin and phospholipid.

A Correspondence-Free Color Chart Design for Color Calibration

2020 ◽  
Vol 2020 (1) ◽  
pp. 100-104
Author(s):  
Hakki Can Karaimer ◽  
Rang Nguyen
Keyword(s):  
Color Space ◽  
Fixed Number ◽  
New Approach ◽  
Color Chart ◽  
Color Calibration ◽  
Space Transformation ◽  
Color Space Transformation ◽  
Chart Design ◽  
Calibration Approach

Colorimetric calibration computes the necessary color space transformation to map a camera's device-specific color space to a device-independent perceptual color space. Color calibration is most commonly performed by imaging a color rendition chart with a fixed number of color patches with known colorimetric values (e. g., CIE XYZ values). The color space transformation is estimated based on the correspondences between the camera's image and the chart's colors. We present a new approach to colorimetric calibration that does not require explicit color correspondences. Our approach computes a color space transformation by aligning the color distributions of the captured image to the known distribution of a calibration chart containing thousands of colors. We show that a histogram-based colorimetric calibration approach provides results that are onpar with the traditional patch-based method without the need to establish correspondences.

A Brief Survey on Text Classification Using Various Machine Learning Techniques

2018 ◽  
Vol 8 (1) ◽  
pp. 14
Author(s):  
Padmavathi .S ◽  
M. Chidambaram
Keyword(s):  
Machine Learning ◽  
Text Classification ◽  
Fixed Number ◽  
Machine Learning Techniques ◽  
Online Information ◽  
Rule Based ◽  
Learning Techniques ◽  
Machine Learning Approach ◽  
Rule Based Approach

Text classification has grown into more significant in managing and organizing the text data due to tremendous growth of online information. It does classification of documents in to fixed number of predefined categories. Rule based approach and Machine learning approach are the two ways of text classification. In rule based approach, classification of documents is done based on manually defined rules. In Machine learning based approach, classification rules or classifier are defined automatically using example documents. It has higher recall and quick process. This paper shows an investigation on text classification utilizing different machine learning techniques.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Evaluation of Mixed Deep Neural Networks for Reverberant Speech Enhancement

Biomimetics ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 1 ◽  
Author(s):  
Michelle Gutiérrez-Muñoz ◽  
Astryd González-Salazar ◽  
Marvin Coto-Jiménez
Keyword(s):  
Neural Networks ◽  
Short Term Memory ◽  
Computational Cost ◽  
Real Life ◽  
Fixed Number ◽  
Training Procedure ◽  
Statistical Validation ◽  
Significant Drop ◽  
Training Time ◽  
Important Solution

Speech signals are degraded in real-life environments, as a product of background noise or other factors. The processing of such signals for voice recognition and voice analysis systems presents important challenges. One of the conditions that make adverse quality difficult to handle in those systems is reverberation, produced by sound wave reflections that travel from the source to the microphone in multiple directions. To enhance signals in such adverse conditions, several deep learning-based methods have been proposed and proven to be effective. Recently, recurrent neural networks, especially those with long short-term memory (LSTM), have presented surprising results in tasks related to time-dependent processing of signals, such as speech. One of the most challenging aspects of LSTM networks is the high computational cost of the training procedure, which has limited extended experimentation in several cases. In this work, we present a proposal to evaluate the hybrid models of neural networks to learn different reverberation conditions without any previous information. The results show that some combinations of LSTM and perceptron layers produce good results in comparison to those from pure LSTM networks, given a fixed number of layers. The evaluation was made based on quality measurements of the signal’s spectrum, the training time of the networks, and statistical validation of results. In total, 120 artificial neural networks of eight different types were trained and compared. The results help to affirm the fact that hybrid networks represent an important solution for speech signal enhancement, given that reduction in training time is on the order of 30%, in processes that can normally take several days or weeks, depending on the amount of data. The results also present advantages in efficiency, but without a significant drop in quality.

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