Study on Parameter Transfer Structure of Generalized Modular Based Graph Theory

2012 ◽  
Vol 562-564 ◽  
pp. 1323-1326 ◽  
Author(s):  
Chao Zhou ◽  
Yan Ping Liu
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Mathematical Description ◽  
Theoretical Basis ◽  
Product Structure ◽  
Decomposition Algorithm ◽  
Modular Structure ◽  
Directed Edge ◽  
Transfer Structure ◽  
Transfer Chain

For the purpose of reducing product structure levels and shorting transfer chain of parameter, in this paper the product structure levels are expressed with generalized modular. The concept of directed graph of parameter connection structure for generalized modular is proposed with the use of directed graph theory, generalized modular, sub-modular and part represented by vertex, the driven relations of parameter connection represented by directed edge, and the properties of directed graph of parameter connection structure for generalized modular are gained. The directed graph of parameter connection structure for generalized modular is divided into a number of sub-graphs according to the relations of product-level modular structure. And the horizontal edges of sub-graphs among vertexes are decomposed. Therefore, a standardized relation of parameter connection structure is established by given the decomposition algorithm and the mathematical description of parameters connection that are provide the theoretical basis for parameters connection analysis of variant design.

A Reliability Analysis Method Based on Execution Scenario for Modular NC Software

2008 ◽  
Vol 392-394 ◽  
pp. 640-644
Author(s):  
Xin Hua Yao ◽  
Jian Zhong Fu ◽  
Zi Chen Chen
Keyword(s):  
Graph Theory ◽  
Reliability Analysis ◽  
Directed Graph ◽  
Software Reliability ◽  
Numerical Control ◽  
Modular Structure ◽  
First Principle ◽  
Analysis Method ◽  
Nc System

To describe the modular structure of numerical control (NC) system and deal with the problem of interference between modules in software reliability analysis, a module dependency graph (MDG) was presented and a scenario-based scheme was proposed. MDG describes reliability of module in different application environment, module dependency and structure of software with establishing maps among modules, execution scenarios and reliability. According to the information shown in MDG, an algorithm based on the idea of traversing directed graph in graph theory was proposed. The algorithm calculates the reliability of scenario with breadth-first principle. The reliability of system could be obtained from reliability and running frequency of scenario. The scheme eliminates the defects of the conventional methods which ignore module correlation. Case study proves the scheme could evaluate the reliability of NC software effectively.

scholarly journals Intrinsic linking and knotting in tournaments

2019 ◽  
Vol 28 (12) ◽  
pp. 1950076
Author(s):  
Thomas Fleming ◽  
Joel Foisy
Keyword(s):  
Directed Graph ◽  
Upper Bound ◽  
Directed Edge ◽  
Undirected Graphs ◽  
Oriented Cycle ◽  
Minimum Number ◽  
The Difference

A directed graph [Formula: see text] is intrinsically linked if every embedding of that graph contains a nonsplit link [Formula: see text], where each component of [Formula: see text] is a consistently oriented cycle in [Formula: see text]. A tournament is a directed graph where each pair of vertices is connected by exactly one directed edge. We consider intrinsic linking and knotting in tournaments, and study the minimum number of vertices required for a tournament to have various intrinsic linking or knotting properties. We produce the following bounds: intrinsically linked ([Formula: see text]), intrinsically knotted ([Formula: see text]), intrinsically 3-linked ([Formula: see text]), intrinsically 4-linked ([Formula: see text]), intrinsically 5-linked ([Formula: see text]), intrinsically [Formula: see text]-linked ([Formula: see text]), intrinsically linked with knotted components ([Formula: see text]), and the disjoint linking property ([Formula: see text]). We also introduce the consistency gap, which measures the difference in the order of a graph required for intrinsic [Formula: see text]-linking in tournaments versus undirected graphs. We conjecture the consistency gap to be nondecreasing in [Formula: see text], and provide an upper bound at each [Formula: see text].

scholarly journals The Diameter of Almost Eulerian Digraphs

10.37236/429 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Peter Dankelmann ◽  
L. Volkmann
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Upper Bound ◽  
Minimum Degree ◽  
Additive Constant ◽  
Undirected Graphs

Soares [J. Graph Theory 1992] showed that the well known upper bound $\frac{3}{\delta+1}n+O(1)$ on the diameter of undirected graphs of order $n$ and minimum degree $\delta$ also holds for digraphs, provided they are eulerian. In this paper we investigate if similar bounds can be given for digraphs that are, in some sense, close to being eulerian. In particular we show that a directed graph of order $n$ and minimum degree $\delta$ whose arc set can be partitioned into $s$ trails, where $s\leq \delta-2$, has diameter at most $3 ( \delta+1 - \frac{s}{3})^{-1}n+O(1)$. If $s$ also divides $\delta-2$, then we show the diameter to be at most $3(\delta+1 - \frac{(\delta-2)s}{3(\delta-2)+s} )^{-1}n+O(1)$. The latter bound is sharp, apart from an additive constant. As a corollary we obtain the sharp upper bound $3( \delta+1 - \frac{\delta-2}{3\delta-5})^{-1} n + O(1)$ on the diameter of digraphs that have an eulerian trail.

A Method for Completeness Testing of Dimensioning in 2D Drawing

2013 ◽  
Vol 319 ◽  
pp. 351-355 ◽  
Author(s):  
Tian Zhong Sui ◽  
Zhen Tan ◽  
Lei Wang ◽  
Xiao Bin Gu ◽  
Zhao Hui Ren
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Effective Algorithm ◽  
Engineering Drawing ◽  
Intelligent Search ◽  
Important Link ◽  
Correct Conclusion ◽  
2D Drawing

Dimensioning work is a considerably important link in the whole Engineering Drawing. For existing completeness testing of dimensioning, correct conclusion can not be drawn in case of multi-closed dimension. This paper mainly discusses the ways how to automatically check up the deficiency and redundancy of the dimensions. This paper presents a new and effective algorithm to test whether the dimensions are redundant or insufficient by means of the graph theory and intelligent search. The dimensions are transformed to non-directed graph, then detects whether they are redundant or insufficient by traversing adjacent matrix of the non-directed graph. The deficiency and redundancy of dimension for multi-views of engineering drawing can be corrected by this algorithm.

Getting a Directed Hamilton Cycle Two Times Faster

2012 ◽  
Vol 21 (5) ◽  
pp. 773-801 ◽  
Author(s):  
CHOONGBUM LEE ◽  
BENNY SUDAKOV ◽  
DAN VILENCHIK
Keyword(s):  
Graph Theory ◽  
Random Graph ◽  
Directed Graph ◽  
Classical Result ◽  
Hamilton Cycle ◽  
Empty Graph ◽  
Underlying Graph ◽  
Random Direction ◽  
Random Graph Theory ◽  
On Line

Consider the random graph process where we start with an empty graph on n vertices and, at time t, are given an edge et chosen uniformly at random among the edges which have not appeared so far. A classical result in random graph theory asserts that w.h.p. the graph becomes Hamiltonian at time (1/2+o(1))n log n. On the contrary, if all the edges were directed randomly, then the graph would have a directed Hamilton cycle w.h.p. only at time (1+o(1))n log n. In this paper we further study the directed case, and ask whether it is essential to have twice as many edges compared to the undirected case. More precisely, we ask if, at time t, instead of a random direction one is allowed to choose the orientation of et, then whether or not it is possible to make the resulting directed graph Hamiltonian at time earlier than n log n. The main result of our paper answers this question in the strongest possible way, by asserting that one can orient the edges on-line so that w.h.p. the resulting graph has a directed Hamilton cycle exactly at the time at which the underlying graph is Hamiltonian.

Formulation of Dimensional Synthesis Procedures for Complex Planar Mechanisms

1987 ◽  
Vol 109 (3) ◽  
pp. 322-328 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Dimensional Synthesis ◽  
Planar Mechanisms

This paper presents an overview of a component-based approach for the dimensional synthesis of planar mechanisms. The components on which the approach is based are called triads, dyads, and free vectors, and can be synthesized for up to five precision positions. A straight-forward method for formulating dimensional synthesis procedures for arbitrarily complex planar mechanisms is developed, and demonstrated by an example using inspection. The method utilizes the concept of the directed graph, which is an enhancement of the usual graph theory representation of mechanisms. Because the method is based on graph theory, it is believed that it could be easily automated.

scholarly journals The Graph of e-Abacus Diagram

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Letter Word ◽  
New Type

Since James introduced the idea of an e-abacus diagram in 1978, this topic plays important roles with many topics, especially in algebra. In this paper, we will present new insights on this topic so that it appears to us as a graph theory; specifically a directed graph, according to certain conditions, to be a new start with another field. This proposed technique will be applied to the model that was approved by Mahmood and Mahmood in 2019 on English letters and to see how successful we are on Letter-Word-Sentence. It is completely natural that this method will have a new and very difficult method as an entrance to a new type of encryption process

scholarly journals APLIKASI ALGORITMA DIJKSTRA UNTUK MENENTUKAN RUTE TERPENDEK DARI KAMPUS A KE B UIN RADEN FATAH

2021 ◽  
Vol 10 (3) ◽  
pp. 173
Author(s):  
RENDI SAPUTRAMA ◽  
HARTATIANA HARTATIANA
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Applied Research ◽  
Dijkstra’S Algorithm ◽  
The Road ◽  
Dijkstra's Algorithm ◽  
Shortest Route ◽  
Starting Point ◽  
Route Option

Finding the shortest direction is one of the options that have been considered while traveling. One of the problems that occur for lecturers, staff, and students of UIN Raden Fatah is determining the shortest direction from Campus A to B. The application of graph theory by using Dijkstra's Algorithm becomes a solution for this problem. This algorithm has the advantage to minimize the expense of the costs by finding the shortest route from starting point to the destination. This study is applied research. The study will discuss the determination of the origin and destination end-point, traverse route, the calculation of the weight distance, analyzes the Dijkstra's iteration to determine the shortest route, and conclusion. As the result, the land route becomes the shortest route option from UIN Raden Fatah Campus A to B. The directed graph of the route represents the location as point, the road as the side, and distance as weight. The result shows that the route distance is 6.94 km using Dijkstra's Algorithm.

scholarly journals Hamiltonicity in random directed graphs is born resilient

2020 ◽  
Vol 29 (6) ◽  
pp. 900-942 ◽  
Author(s):  
Richard Montgomery
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Directed Edge

AbstractLet $\{D_M\}_{M\geq 0}$ be the n-vertex random directed graph process, where $D_0$ is the empty directed graph on n vertices, and subsequent directed graphs in the sequence are obtained by the addition of a new directed edge uniformly at random. For each $$\varepsilon > 0$$ , we show that, almost surely, any directed graph $D_M$ with minimum in- and out-degree at least 1 is not only Hamiltonian (as shown by Frieze), but remains Hamiltonian when edges are removed, as long as at most $1/2-\varepsilon$ of both the in- and out-edges incident to each vertex are removed. We say such a directed graph is $(1/2-\varepsilon)$ -resiliently Hamiltonian. Furthermore, for each $\varepsilon > 0$ , we show that, almost surely, each directed graph $D_M$ in the sequence is not $(1/2+\varepsilon)$ -resiliently Hamiltonian.This improves a result of Ferber, Nenadov, Noever, Peter and Škorić who showed, for each $\varepsilon > 0$ , that the binomial random directed graph $D(n,p)$ is almost surely $(1/2-\varepsilon)$ -resiliently Hamiltonian if $p=\omega(\log^8n/n)$ .

Network Modeling

2010 ◽  
pp. 113-121 ◽  
Author(s):  
Kevin M. Curtin
Keyword(s):  
Graph Theory ◽  
Theoretical Basis ◽  
Network Modeling ◽  
Network Models ◽  
Data Models ◽  
Flow Modeling ◽  
Important Data ◽  
Network Analyses ◽  
Topological Relationships ◽  
Mathematical Discipline

Network models are some of the earliest and most consistently important data models in GISystems. Network modeling has a strong theoretical basis in the mathematical discipline of graph theory, and methods for describing and measuring networks and proving properties of networks are well-developed. There are a variety of network models in GISystems, which are primarily differentiated by the topological relationships they maintain. Network models can act as the basis for location through the process of linear referencing. Network analyses such as routing and flow modeling have to some extent been implemented, although there are substantial opportunities for additional theoretical advances and diversified application.

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