scholarly journals On Average Distance of Neighborhood Graphs and Its Applications

2021 ◽  
Author(s):  
Elias Mwakilama ◽  
Patrick Ali ◽  
Patrick Chidzalo ◽  
Kambombo Mtonga ◽  
Levis Eneya
Keyword(s):  
Bipartite Graph ◽  
Connected Graph ◽  
Average Distance ◽  
Distance Measures ◽  
Graph Invariants ◽  
Matlab Software ◽  
Software Simulation ◽  
Neighborhood Graph ◽  
Research Questions ◽  
Simulation Results

Graph invariants such as distance have a wide application in life, in particular when networks represent scenarios in form of either a bipartite or non-bipartite graph. Average distance μ of a graph G is one of the well-studied graph invariants. The graph invariants are often used in studying efficiency and stability of networks. However, the concept of average distance in a neighborhood graph G′ and its application has been less studied. In this chapter, we have studied properties of neighborhood graph and its invariants and deduced propositions and proofs to compare radius and average distance measures between G and G′. Our results show that if G is a connected bipartite graph and G′ its neighborhood, then radG1′≤radG and radG2′≤radG whenever G1′ and G2′ are components of G′. In addition, we showed that radG′≤radG for all r≥1 whenever G is a connected non-bipartite graph and G′ its neighborhood. Further, we also proved that if G is a connected graph and G′ its neighborhood, then and μG1′≤μG and μG2′≤μG whenever G1′ and G2′ are components of G′. In order to make our claims substantial and determine graphs for which the bounds are best possible, we performed some experiments in MATLAB software. Simulation results agree very well with the propositions and proofs. Finally, we have described how our results may be applied in socio-epidemiology and ecology and then concluded with other proposed further research questions.

Simulation of Magnetically Controlled Reactors Based on MATLAB

2014 ◽  
Vol 599-601 ◽  
pp. 1064-1067
Author(s):  
Peng Kang Xie ◽  
Guo Zhu Chen
Keyword(s):  
Power System ◽  
Power Control ◽  
Reactive Power ◽  
Operating Characteristics ◽  
Reactive Power Control ◽  
Matlab Software ◽  
Software Simulation ◽  
Fast Development ◽  
Working Principle ◽  
Simulation Results

Nowadays, with the fast development of power system, reactive power control has become a hot topic. As a kind of reactive power control equipment, magnetically controlled reactor (MCR) has been widely concerned and researched. This paper analyzed the working principle of MCR by mathematic method, built the circuit model in MATLAB software. Simulation results show the operating characteristics of MCR.

scholarly journals Relationships between some distance-based topological indices

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5809-5815 ◽  
Author(s):  
Hongbo Hua ◽  
Ivan Gutman ◽  
Hongzhuan Wang ◽  
Kinkar Das
Keyword(s):  
Connected Graph ◽  
Average Distance ◽  
Topological Indices ◽  
Graph Invariants ◽  
Harary Index ◽  
Eccentricity Index ◽  
Polarity Index ◽  
The Relationship

The Harary index (HI), the average distance (AD), the Wiener polarity index (WPI) and the connective eccentricity index (CEI) are distance-based graph invariants, some of which found applications in chemistry. We investigate the relationship between HI, AD, and CEI, and between WPI, AD, and CEI. First, we prove that HI > AD for any connected graph and that HI > CEI for trees, with only three exceptions. We compare WPI with CEI for trees, and give a classification of trees for which CEI ? WPI or CEI < WPI. Furthermore, we prove that for trees, WPI > AD, with only three exceptions.

Study on Micro-Fracture Chaotic Evolution under External Loading Rock

2013 ◽  
Vol 813 ◽  
pp. 355-358 ◽  
Author(s):  
Ting Ting Wang ◽  
Wan Chun Zhao ◽  
Yuan Hong Liu ◽  
Li Yang ◽  
Hong Yu Gao
Keyword(s):  
Finite Element ◽  
Chaos Theory ◽  
Formation Process ◽  
Theoretical Calculations ◽  
Growth Behavior ◽  
External Loading ◽  
Software Simulation ◽  
Finite Element Software ◽  
Fracture Formation ◽  
Simulation Results

In order to accurately describe the growth behavior of the micro-fracture under the action of the rock external load, this paper proposes the use of chaos theory to describe the fracture formation process, explains the chaotic characteristics of the fracture from the perspective of the growth of micro-fracture, the number of growth and fracture formation morphology, respectively. Selecting the practical block of an oilfield, the theoretical calculation and finite element software simulation results show that, theoretical calculations are accurate and reliable.

scholarly journals Pelabelan 0-Anti Ajaib dan 2-Anti Ajaib untuk Graf Tangga L

2016 ◽  
Vol 12 (1) ◽  
pp. 63
Author(s):  
Quinoza Guvil ◽  
Roni Tri Putra
Keyword(s):  
Bipartite Graph ◽  
Connected Graph ◽  
Partition Dimension ◽  
Dimension Partition

For a connected graph  and a subset  of   . For a vertex  the distance betwen  and  is . For an ordered k-partition of ,  the representation of   with respect to  is    The k-partition  is a resolving partition if  are distinct for every  The minimum k for which there is a resolving partition of   is the partition dimension of   In this paper will shown resolving partition of  connected graph order  where  is a bipartite graph. Then it is shown dimension partition of bipartite graph, are pd(Kst)=n-1

OPNET-Based Computer Simulation of MPLS VPN Security Solutions

2010 ◽  
Vol 40-41 ◽  
pp. 361-365
Author(s):  
Ya Qin Fan ◽  
Hao Fan ◽  
Chao Sun
Keyword(s):  
Computer Simulation ◽  
Information Disclosure ◽  
Reference Value ◽  
Simulation System ◽  
Simulation Software ◽  
Software Simulation ◽  
The Public ◽  
Backbone Network ◽  
Mpls Vpn ◽  
Simulation Results

This paper features of IPSec and MPLS technologies, proposes a suitable MPLS VPN security solutions. The program to solve the VPN using MPLS backbone network in the public transport there is a second layer of information can not automatically encrypt, or connect easily made because of errors due to the interruption of information disclosure and other issues. To verify the proposed security program, the actual MPLS VPN can be simplified, abstracestablishing a simulation system MPLS VPN, and using OPNET simulation software simulation, simulation results of VPN officers practical reference value.

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

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 Size effect of Water-flowing fracture Zone height based on FLAC3D

2020 ◽  
Vol 194 ◽  
pp. 01011
Author(s):  
Chao Zheng ◽  
Lan Yu ◽  
Ning Sun ◽  
Hualong Zhou ◽  
Jiangyi He
Keyword(s):  
Size Effect ◽  
Coal Mine ◽  
Fracture Zone ◽  
Average Distance ◽  
Water Inrush ◽  
Water Diversion ◽  
Effect Of Water ◽  
Face Width ◽  
Working Face ◽  
Simulation Results

The loss of water resources caused by mining fissures is a key factor restricting the green development of coal resources in western mining areas. in order to analyze the influence of mining thickness and face width on the development height of water diversion fracture zone, based on the characteristics of overburden in Xinzhuang Coal Mine, the finite difference software FLAC3D is used to simulate and analyze the size effect of water diversion fracture zone height. The simulation results show that the height of the water diversion fracture zone is positively correlated with the increase of mining thickness and working face width. When the mining thickness is 9m and the width of the working face is 240m, the height of the water diversion fracture zone is 115m, and the average distance between the coal layer 8 of Xinzhuang Coal Mine and the bottom of the Cretaceous aquifer is 106.9m, which may cause water inrush in the mine. Therefore, according to the simulation results and referring to the mining size of part of the mine face in the attached Binchang mining area, it is suggested that the mining thickness of Xinzhuang Coal Mine is about 10m and the width of the working face is not more than 200m.

Design and Analysis of Thermoacoustic Refrigerators Using Air as Working Substance

2019 ◽  
Vol 27 (01) ◽  
pp. 1950008 ◽  
Author(s):  
B. G. Prashantha ◽  
S. Seetharamu ◽  
G. S. V. L. Narasimham ◽  
M. R. Praveen Kumar
Keyword(s):  
Heat Exchanger ◽  
Heat Exchangers ◽  
Low Cost ◽  
Design Strategies ◽  
Software Simulation ◽  
Design And Optimization ◽  
Theoretical Design ◽  
Resonator Design ◽  
Simulation Results ◽  
Thermoacoustic Refrigerators

In this paper, the design of 50 W thermoacoustic refrigerators operating with air as working substance at 10 bar pressure and 3% drive ratio for a temperature difference of 28 K is described. The design strategies discussed in this paper help in design and development of low cost thermoacoustic coolers compared to helium as the working substance. The design and optimization of spiral stack and heat exchangers, and the promising 0.2[Formula: see text] and 0.15[Formula: see text] resonator design with taper and divergent section with hemispherical end are discussed. The surface area, volume, length and power density of the hemispherical end design with air as working substance is found better compared to the published 10 and 50 W coolers using helium as the working substance. The theoretical design results are validated using DeltaEC software simulation results. The DeltaEC predicts 51.4% improvement in COP (1.273) at the cold heat exchanger temperature of [Formula: see text]C with air as working substance for the 50[Formula: see text]W 0.15[Formula: see text]TDH resonator design compared to the published 50[Formula: see text]W 0.25[Formula: see text]TDH resonator design with helium as working substance.

Energy Optimization at GSM Base Station Sites Located in Rural Areas

2012 ◽  
Vol 1 (3) ◽  
pp. 1-31 ◽  
Author(s):  
Vincent Anayochukwu Ani ◽  
Nzeako Anthony Ndubueze
Keyword(s):  
Rural Areas ◽  
Base Station ◽  
Base Stations ◽  
Software Simulation ◽  
Simulation Results ◽  
Energy Options ◽  
Total Impact ◽  
Geographical Locations ◽  
Station Site ◽  
Mobile Base

This paper explores the best energy options by which the choice of the most energy optimized solution for a given GSM Base Station Site and location in any rural area in Nigeria can be made. The patterns of load consumption by mobile base stations at various geographical locations in rural areas are studied and suitably modeled for optimization using HOMER software. Simulation results show the optimized energy options to be superior to conventional solutions whereby diesel generators are currently used to power GSM Base Station Sites around Nigeria. Total Net Present Cost (NPC) and total impact on the environment are used as indices for measuring the optimization level of each energy solution. The solution with the highest optimization value is considered to be the best energy option for that Base Station Site.

Sign in / Sign up

Export Citation Format

Share Document