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.

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.

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.

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.

scholarly journals The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Fatih Yılmaz ◽  
Durmuş Bozkurt
Keyword(s):  
Graph Theory ◽  
Positive Integer ◽  
Directed Graph ◽  
Adjacency Matrix ◽  
Intensive Study ◽  
Integer Power ◽  
Determinantal Representation ◽  
Adjacency Matrices

Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph. By using the well-known property which states the(i,j)entry ofAm(Ais adjacency matrix) is equal to the number of walks of lengthmfrom vertexito vertexj, we show that elements ofmth positive integer power of the adjacency matrix correspond to well-known Jacobsthal numbers. As a consequence, we give a Cassini-like formula for Jacobsthal numbers. We also give a matrix whose permanents are Jacobsthal numbers.

Development of methodology for the disassemblability index of automobile systems using a structural approach

2016 ◽  
Vol 231 (4) ◽  
pp. 516-535 ◽  
Author(s):  
Ajith Tom James ◽  
Om Parkash Gandhi ◽  
Sanjeev Govindrao Deshmukh
Keyword(s):  
Graph Theory ◽  
Directed Graph ◽  
Contextual Factors ◽  
Structural Approach ◽  
Step Procedure ◽  
Index Ratio ◽  
Alternative Designs ◽  
Design Factors ◽  
The Ideal

The time and effort required for maintenance of an automobile system are highly dependent on its disassemblability, which is one of the most important attributes of its maintainability. To evaluate the disassemblability index, i.e. to measure the ease of disassembly, the disassemblability factors (both the design factors and the contextual factors) of an automobile system are identified. These and their interrelations are modelled by considering their structure using the graph theory. The directed graph (digraph) of the disassemblability of the automobile system is defined; the nodes of this represent its disassemblability factors, while the edges represent their degrees of influence. An equivalent matrix of the digraph establishes the system’s disassemblability function which characterizes the disassemblability of the system, leading to development of the disassemblability index. A high value of the disassemblability index indicates that it is very easy to remove or replace parts. The disassemblability index ratio is used to compare the actual conditions of disassembly with the ideal conditions of disassembly. A case study of an automobile gearbox is illustrated using the step-by-step procedure of the proposed methodology of disassemblability. The proposed methodology is helpful to evaluate and compare various alternative designs of the automobile system and, therefore, can aid the design and development of automobile systems from the disassembly viewpoint.

Development of a design based remanufacturability index for automobile systems

2021 ◽  
pp. 095440702110055
Author(s):  
Ajith Tom James ◽  
Girish Kumar ◽  
Aavriti Arora ◽  
Shrey Padhi
Keyword(s):  
Graph Theory ◽  
Environmental Protection ◽  
Product Design ◽  
End Of Life ◽  
Directed Graph ◽  
High Potential ◽  
Design Stage ◽  
Matrix Approach ◽  
Technical Feasibility ◽  
Design Attributes

The growing concern over environmental protection is prompting automobile manufacturers to develop products with better End-of-Life performance. Product remanufacturability is considered as an End-of-Life performance booster. Remanufacturability, that is, the easiness for remanufacturing of products depends on the technical, environmental, and economic feasibilities. The technical feasibility depends on the product design attributes that support remanufacturability. These design attributes are comprised of several sub-attributes. Moreover, the attributes are interrelated with each other. This paper develops a remanufacturability index for automobile systems based on the design attributes that affect the remanufacturability. A structural methodology of graph theory and matrix approach is applied for developing the remanufacturability index. The design attributes and their interrelations with due consideration of their structure is modelled through the graph theory. The remanufacturability directed graph (digraph) is defined; the nodes of this represent the remanufacturability enhancing design attributes, while the edges represent their degrees of interrelationships. The equivalent matrix of the digraph forms a remanufacturability function which leads to the evaluation of remanufacturability index. A higher value of the remanufacturability index indicates that the automobile system has high potential for being remanufactured. The methodology can be applied during the design stage of automobile systems to evaluate the remanufacturability that will enhance the End-of-Life performance. The observations would be helpful to automobile system designers in determining the extent to which the system can be remanufactured and in identifying the specific attributes that can be improved to enhance remanufacturability.

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