scholarly journals Asymptotically Effective Method to Explore Euler Path in a Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Muhammad Fahad ◽  
Sikandar Ali ◽  
Mukhtaj Khan ◽  
Mujtaba Husnain ◽  
Zeeshan Shafi ◽  
...  
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Computation Complexity ◽  
Eulerian Graphs ◽  
Euler Path ◽  
Simulation Results ◽  
Euler Graph

Euler path is one of the most interesting and widely discussed topics in graph theory. An Euler path (or Euler trail) is a path that visits every edge of a graph exactly once. Similarly, an Euler circuit (or Euler cycle) is an Euler trail that starts and ends on the same node of a graph. A graph having Euler path is called Euler graph. While tracing Euler graph, one may halt at arbitrary nodes while some of its edges left unvisited. In this paper, we have proposed some precautionary steps that should be considered in exploring a deadlock-free Euler path, i.e., without being halted at any node. Simulation results show that our proposed approach improves the process of exploring the Euler path in an undirected connected graph without interruption. Furthermore, our proposed algorithm is complete for all types of undirected Eulerian graphs. The paper concludes with the proofs of the correctness of proposed algorithm and its computation complexity.

scholarly journals Multiplicative Zagreb indices of cacti

2016 ◽  
Vol 08 (03) ◽  
pp. 1650040 ◽  
Author(s):  
Shaohui Wang ◽  
Bing Wei
Keyword(s):  
Graph Theory ◽  
Lower Bounds ◽  
Connected Graph ◽  
Upper And Lower Bounds ◽  
Extremal Graphs ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Material Chemistry ◽  
Cactus Graph ◽  
Cactus Graphs

Let [Formula: see text] be multiplicative Zagreb index of a graph [Formula: see text]. A connected graph is a cactus graph if and only if any two of its cycles have at most one vertex in common, which is a generalization of trees and has been the interest of researchers in the field of material chemistry and graph theory. In this paper, we use a new tool to obtain the upper and lower bounds of [Formula: see text] for all cactus graphs and characterize the corresponding extremal graphs.

scholarly journals Logistics management of the rail connections using graph theory: the case of a public transportation company on the example of Koleje Dolnośląskie S.A.

2018 ◽  
Vol 10 (3) ◽  
pp. 7-22
Author(s):  
Paweł Sobczak ◽  
Ewa Stawiarska ◽  
Judit Oláh ◽  
József Popp ◽  
Tomas Kliestik
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Public Transportation ◽  
Transportation Networks ◽  
Logistics Management ◽  
Simulation Methods ◽  
Southern Poland ◽  
Transport Services ◽  
Network Simulations ◽  
Simulation Results

Abstract The main purpose of the paper was the structural analysis of the connections network used by a railway carrier Koleje Dolnośląskie S.A. operating in southern Poland. The analysis used simulation methods. The analysis and simulation were based on graph theory, which is successfully used in analysing a wide variety of networks (social, biological, computer, virtual and transportation networks). The paper presents indicators which allow judging the analysed connections network according to an appropriate level of transport services. Simulation results allowed proposing some modifications for the improvement of the analysed connections network. The paper also demonstrates that graph theory and network simulations should be used as tools by transportation companies during the stage of planning a connections network.

scholarly journals Variational Bayesian Based Adaptive Shifted Rayleigh Filter for Bearings-Only Tracking in Clutters

Sensors ◽  
2019 ◽  
Vol 19 (7) ◽  
pp. 1512 ◽  
Author(s):  
Jing Hou ◽  
Yan Yang ◽  
Tian Gao
Keyword(s):  
Target Tracking ◽  
Data Association ◽  
Tracking Performance ◽  
Computation Complexity ◽  
Variational Bayesian ◽  
Target State ◽  
Scenarios Simulation ◽  
Simulation Results

This paper considers bearings-only target tracking in clutters with uncertain clutter probability. The traditional shifted Rayleigh filter (SRF), which assumes known clutter probability, may have degraded performance in challenging scenarios. To improve the tracking performance, a variational Bayesian-based adaptive shifted Rayleigh filter (VB-SRF) is proposed in this paper. The target state and the clutter probability are jointly estimated to account for the uncertainty in clutter probability. Performance of the proposed filter is evaluated by comparing with SRF and the probability data association (PDA)-based filters in two scenarios. Simulation results show that the proposed VB-SRF algorithm outperforms the traditional SRF and PDA-based filters especially in complex adverse scenarios in terms of track continuity, track accuracy and robustness with a little higher computation complexity.

Image Segmentation Arithmetic Based on Narrow Band C-V

2010 ◽  
Vol 108-111 ◽  
pp. 1338-1343
Author(s):  
Xiao Hu Lv ◽  
Yong Xin Liu
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Narrow Band ◽  
Segmentation Algorithm ◽  
Computational Method ◽  
Computation Complexity ◽  
Iterative Computation ◽  
Iterative Calculation ◽  
Simulation Results

The characters of C-V model are analyzed in this paper. Using the C-V technique to segment objects from an image, every pixel of whole image needed to be updated in each iterative calculation. The amount of iterative calculation is very large. So a computational method combine C-V model with the narrow band of level set is proposed. The segmentation iterative computation is defined on a narrow band, so the computation complexity is gotten lower. This segmentation algorithm is simulated in MATLAB. The simulation results shows that this segment arithmetic is efficiency, constringency fast and can get object integrally.

A Min-Sum Algorithm Suitable for Hardware Implementation Based on LDPC Codes

2011 ◽  
Vol 271-273 ◽  
pp. 458-463
Author(s):  
Rui Ping Chen ◽  
Zhong Xun Wang ◽  
Xin Qiao Yu
Keyword(s):  
Hardware Implementation ◽  
Ldpc Codes ◽  
Low Complexity ◽  
Scaling Factor ◽  
Computation Complexity ◽  
Decoding Complexity ◽  
Decoding Algorithms ◽  
Hardware Resource ◽  
Simulation Results ◽  
Ber Performance

Decoding algorithms with strong practical value not only have good decoding performance, but also have the computation complexity as low as possible. For this purpose, the paper points out the modified min-sum decoding algorithm(M-MSA). On the condition of no increasing in the decoding complexity, it makes the error-correcting performance improved by adding the appropriate scaling factor based on the min-sum algorithm(MSA), and it is very suitable for hardware implementation. Simulation results show that this algorithm has good BER performance, low complexity and low hardware resource utilization, and it would be well applied in the future.

scholarly journals The Partition Dimension of a Path Graph

2021 ◽  
Vol 13 (2) ◽  
pp. 66
Author(s):  
Vivi Ramdhani ◽  
Fathur Rahmi
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Ordered Set ◽  
Minimum Cardinality ◽  
Path Graph ◽  
Partition Dimension

Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph  and  is a subset of  writen . Suppose there is , then the distance between and  is denoted in the form . There is an ordered set of -partitions of, writen then  the representation of with respect tois the  The set of partitions ofis called a resolving partition if the representation of each  to  is different. The minimum cardinality of the solving-partition to  is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitions of path graph,  with ,  and  are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely pd (Pn)=2Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph  and  is a subset of  writen . Suppose there is , then the distance between and  is denoted in the form . There is an ordered set of -partitions of, writen then  the representation of with respect tois the  The set of partitions ofis called a resolving partition if the representation of each  to  is different. The minimum cardinality of the solving-partition to  is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitionsof path graph, with ,  and  are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely.

scholarly journals On the Edge Metric Dimension of Certain Polyphenyl Chains

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Muhammad Ahsan ◽  
Zohaib Zahid ◽  
Dalal Alrowaili ◽  
Aiyared Iampan ◽  
Imran Siddique ◽  
...  
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Metric Dimension ◽  
Chain Graph ◽  
Minimum Number ◽  
Valence Bonds

The most productive application of graph theory in chemistry is the representation of molecules by the graphs, where vertices and edges of graphs are the atoms and valence bonds between a pair of atoms, respectively. For a vertex w and an edge f = c 1 c 2 of a connected graph G , the minimum number from distances of w with c 1 and c 2 is called the distance between w and f . If for every two distinct edges f 1 , f 2 ∈ E G , there always exists w 1 ∈ W E ⊆ V G such that d f 1 , w 1 ≠ d f 2 , w 1 , then W E is named as an edge metric generator. The minimum number of vertices in W E is known as the edge metric dimension of G . In this paper, we calculate the edge metric dimension of ortho-polyphenyl chain graph O n , meta-polyphenyl chain graph M n , and the linear [n]-tetracene graph T n and also find the edge metric dimension of para-polyphenyl chain graph L n . It has been proved that the edge metric dimension of O n , M n , and T n is bounded, while L n is unbounded.

scholarly journals Erdos – Renyi Random Graph and Machine Learning Based Botnet Detection

2020 ◽  
Vol 9 (5) ◽  
pp. 1037-1040
Keyword(s):  
Machine Learning ◽  
Probability Theory ◽  
Graph Theory ◽  
Complex Network ◽  
Random Graphs ◽  
Connected Graph ◽  
Free Graph ◽  
Botnet Detection ◽  
Scale Free ◽  
Made In

Basically large networks are prone to attacks by bots and lead to complexity. When the complexity occurs then it is difficult to overcome the vulnerability in the network connections. In such a case, the complex network could be dealt with the help of probability theory and graph theory concepts like Erdos – Renyi random graphs, Scale free graph, highly connected graph sequences and so on. In this paper, Botnet detection using Erdos – Renyi random graphs whose patterns are recognized as the number of connections that the vertices and edges made in the network is proposed. This paper also presents the botnet detection concepts based on machine learning.

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.

scholarly journals Sequence variations of the 1-2-3 conjecture and irregularity strength

2013 ◽  
Vol Vol. 15 no. 1 (Graph Theory) ◽  
Author(s):  
Ben Seamone ◽  
Brett Stevens
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Minimum Degree ◽  
List Size ◽  
Edge Weighting ◽  
Incident Edge ◽  
Sequence Variations ◽  
Distinct Sequence ◽  
International Audience ◽  
Irregularity Strength

Graph Theory International audience Karonski, Luczak, and Thomason (2004) conjecture that, for any connected graph G on at least three vertices, there exists an edge weighting from 1, 2, 3 such that adjacent vertices receive different sums of incident edge weights. Bartnicki, Grytczuk, and Niwcyk (2009) make a stronger conjecture, that each edge's weight may be chosen from an arbitrary list of size 3 rather than 1, 2, 3. We examine a variation of these conjectures, where each vertex is coloured with a sequence of edge weights. Such a colouring relies on an ordering of E(G), and so two variations arise - one where we may choose any ordering of E(G) and one where the ordering is fixed. In the former case, we bound the list size required for any graph. In the latter, we obtain a bound on list sizes for graphs with sufficiently large minimum degree. We also extend our methods to a list variation of irregularity strength, where each vertex receives a distinct sequence of edge weights.

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