scholarly journals Application of Reverse Vertex Magic Labeling of a Graph

2019 ◽  
Vol 8 (11) ◽  
pp. 12-14
Keyword(s):  
Graph Theory ◽  
Graph Labeling ◽  
The Given ◽  
Positive Integers ◽  
A Company

Graph labeling is a currently emerging area in the research of graph theory. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. If the labels of edges are distinct positive integers and for each vertex the sum of the labels of all edges incident with is the same for every vertex in the given graph, then the labeling of the graph is called magic labeling. There are several types of magic labeling defined on graphs. In this paper we consider vertex magic labeling and group magic labeling of graphs as an application of magic labeling. We solve a problem of finding number of computers/workstations to be allocated to each department in a company under certain conditions.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

An Algorithm for the Enumeration of Serial and/or Parallel Combinations of Kinematic Building Blocks

2004 ◽  
Author(s):  
Hong-Sen Yan ◽  
Feng-Ming Ou ◽  
Ming-Feng Tang
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Power Source ◽  
Cam Follower ◽  
Tree Representations ◽  
The Given

An algorithm is presented, based on graph theory, for enumerating all feasible serial and/or parallel combined mechanisms from the given rotary or translational power source and specific kinematic building blocks. Through the labeled out-tree representations for the configurations of combined mechanisms, the enumeration procedure is developed by adapting the algorithm for the enumeration of trees. A rotary power source and four kinematic building blocks: a crank-rocker linkage, a rack-pinion, a double-slider mechanism, and a cam-follower mechanism, are chosen as the combination to illustrate the algorithm. And, two examples are provided to validate the algorithm.

scholarly journals Graph Theoretic Techniques in the Analysis of Uniquely Localizable Sensor Networks

2009 ◽  
pp. 146-173 ◽  
Author(s):  
Bill Jackson ◽  
Tibor Jordán
Keyword(s):  
Graph Theory ◽  
Sensor Networks ◽  
Optimization Problems ◽  
Partial Information ◽  
Two Dimensions ◽  
Localization Problem ◽  
Graph Theoretic ◽  
Network Localization ◽  
Exact Location ◽  
The Given

In the network localization problem the goal is to determine the location of all nodes by using only partial information on the pairwise distances (and by computing the exact location of some nodes, called anchors). The network is said to be uniquely localizable if there is a unique set of locations consistent with the given data. Recent results from graph theory and combinatorial rigidity made it possible to characterize uniquely localizable networks in two dimensions. Based on these developments, extensions, related optimization problems, algorithms, and constructions also became tractable. This chapter gives a detailed survey of these new results from the graph theorist’s viewpoint.

scholarly journals METHODOLOGY FOR DESIGNING AN EDUCATIONAL SUBSYSTEM AS A POLL FROM THE HOUSE OF QUALITY IN MACEDONIAN COMPANIES

2012 ◽  
Vol 3 (1) ◽  
pp. 81-90
Author(s):  
Elizabeta Mitreva
Keyword(s):  
Collective Learning ◽  
Quality System ◽  
House Of Quality ◽  
Total Quality ◽  
Management Philosophy ◽  
Continued Education ◽  
The Individual ◽  
The Given ◽  
A Company ◽  
Satisfactory Manner

The education of the employees in each instance of a company comes along with a purpose to gain competence and experience in order to realize every business process according to the demands of the products/services, the legal obligation as well as the criteria of competitiveness. Furthermore, it is directly conjoined with the very act of foundation setting of the employees’ requests with a unique intention - to achieve quality, stressing the vital need to affiliate everyone in their own field. This analysis presents the research inputs which are being given in order to get a clear picture whether the Macedonian companies are eager to learn and stimulate both the individual and the collective learning in order to improve the results in general. According to the given results in the research, it is stated that the Macedonian companies do not pay much attention to quality. They are insufficiently concerned with the continuous education, which is evident in the small investments they make in regard to the innovations. Hence, the quality system has been built in a very small number of companies. The following model presented in this elaborate has been suggested for a more successful designing and implementation of the educational system as a subsystem of the house of quality. This methodology is integral and has a universal notion which is applicable to all types of companies and institutions as well. Without a conducted training about TQM (Total Quality Management) philosophy and a continued education provided firstly for the managers and further on for all of the employees, the TQM strategy could not be implemented in a satisfactory manner. Also, the benefits that come along with the quality system could not be visible as a result. Key words: educational subsystem, leadership, methodology, quality system, TQM strategy.

scholarly journals Cryptosystem using double vertex graph

2020 ◽  
Vol 13 (44) ◽  
pp. 4483-4489
Author(s):  
C Beaula ◽  
Keyword(s):  
Graph Theory ◽  
Secure Communication ◽  
System Method ◽  
Encryption And Decryption ◽  
Vertex Graph ◽  
Private And Public ◽  
Almost All ◽  
Encryption Method ◽  
The Given ◽  
Edge Labeling

Background/Objective: The Coronavirus Covid-19 has affected almost all the countries and millions of people got infected and more deaths have been reported everywhere. The uncertainty and fear created by the pandemic can be used by hackers to steal the data from both private and public systems. Hence, there is an urgent need to improve the security of the systems. This can be done only by building a strong cryptosystem. So many researchers started embedding different topics of mathematics like algebra, number theory, and so on in cryptography to keep the system, safe and secure. In this study, a cryptosystem using graph theory has been attempted, to strengthen the security of the system. Method: A new graph is constructed from the given graph, known as a double vertex graph. The edge labeling of this double vertex graph is used in encryption and decryption. Findings: A new cryptosystem using the amalgamation of the path, its double vertex graph and edge labeling has been proposed. From the double vertex graph of a path, we have given a method to find the original path. To hack such an encrypted key, the knowledge of graph theory is important, which makes the system stronger. Applications:The one-word encryption method will be useful in every security system that needs a password for secure communication or storage or authentication. Keywords: Double vertex graphs; path; adjacency matrix; encryption; cryptography

scholarly journals Sun Toughness Conditions for P 2 and P 3 Factor Uniform and Factor Critical Avoidable Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shu Gong ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
The Sun ◽  
Graph Structure ◽  
Network Graph ◽  
The Given ◽  
Path Factor

The security of a network is closely related to the structure of the network graph. The denser the network graph structure is, the better it can resist attacks. Toughness and isolated toughness are used to characterize the vulnerable programs of the network which have been paid attention from mathematics and computer scholars. On this basis, considering the particularity of the sun component structures, sun toughness was introduced in mathematics and applied to computer networks. From the perspective of modern graph theory, this paper presents the sun toughness conditions of the path factor uniform graph and the path factor critical avoidable graph in P ≥ 2 -factor and P ≥ 3 -factor settings. Furthermore, examples show that the given boundaries are sharp.

scholarly journals On Study of Vertex Labeling of Graph Operations

2011 ◽  
Vol 3 (2) ◽  
pp. 291-301
Author(s):  
M. A. Rajan ◽  
N. M. Kembhavimath ◽  
V. Lokesha
Keyword(s):  
Direct Product ◽  
Graph Labeling ◽  
Natural Numbers ◽  
Graph Vertex ◽  
Direct Sum ◽  
Graph Operations ◽  
Subdivision Graph ◽  
Maximal Vertex ◽  
The Given

Vertices of the graphs are labeled from the set of natural numbers from 1 to the order of the given graph. Vertex adjacency label set (AVLS) is the set of ordered pair of vertices and its corresponding label of the graph. A notion of vertex adjacency label number (VALN) is introduced in this paper. For each VLS, VLN of graph is the sum of labels of all the adjacent pairs of the vertices of the graph. is the maximum number among all the VALNs of the  different labeling of the graph and the corresponding VALS is defined as maximal vertex  adjacency label set . In this paper  for different graph operations are discussed. Keywords: Subdivision; Graph labeling; Direct sum; Direct product.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i26222                  J. Sci. Res. 3 (2), 291-301 (2011) 

scholarly journals Graceful Labeling of Hypertrees

2021 ◽  
Vol 13 (1) ◽  
pp. 28
Author(s):  
H. El-Zohny ◽  
S. Radwan ◽  
S.I. Abo El-Fotooh ◽  
Z. Mohammed
Keyword(s):  
Graph Theory ◽  
Simple Graph ◽  
Graph Labeling ◽  
Graceful Labeling ◽  
Edge Labeling

Graph labeling is considered as one of the most interesting areas in graph theory. A labeling for a simple graph G (numbering or valuation), is an association of non -negative integers to vertices of G  (vertex labeling) or to edges of G  (edge labeling) or both of them. In this paper we study the graceful labeling for the k- uniform hypertree and define a condition for the corresponding tree to be graceful. A k- uniform hypertree is graceful if the minimum difference of vertices’ labels of each edge is distinct and each one is the label of the corresponding edge.

Milling Simulation-Based Method to Evaluate Manufacturability of Machine Parts

2020 ◽  
Author(s):  
Masatomo Inui ◽  
Tong Zhang ◽  
Nobuyuki Umezu
Keyword(s):  
Graphics Processing Unit ◽  
Cutting Tools ◽  
Processing Unit ◽  
Milling Simulation ◽  
Milling Operations ◽  
Simulation Based ◽  
Mechanical Products ◽  
Graphics Processing ◽  
The Given ◽  
A Company

Abstract The designers of mechanical products are generally not experts in machining. Therefore, they often design parts with inherent machining difficulties. Although various design for manufacturability tools have been developed to avoid such problems, their use in practice remains limited due to their lack of versatility. We develop a novel piece of software that can automatically detect difficult-to-machine shapes in a part. Using this software, the designer can determine which shapes are difficult to produce using conventional cutting by themselves, and can modify the shape on the spot. In the Internet-based part manufacturing business, the same software can be used to check whether the given part can be produced using the standard milling operations predetermined in a company. Our system is based on “milling simulation”. It detects any shapes that cannot be produced using the prepared cutting tools by executing the milling simulations with the tools, and then visualizing shapes that remain unmachined after all simulations. In this study, the acceleration of the processing is realized using graphics processing unit technology, and it is possible to extract difficult-to-machine shapes in several minutes using a standard PC.

Total Irregularity Strengths of an Arbitrary Disjoint Union of (3,6)- Fullerenes

2020 ◽  
Vol 23 ◽  
Author(s):  
Ayesha Shabbir ◽  
Muhammad Faisal Nadeem ◽  
Mohammad Ovais ◽  
Faraha Ashraf ◽  
Sumiya Nasir
Keyword(s):  
Graph Theory ◽  
Lower Bound ◽  
Coding Theory ◽  
Disjoint Union ◽  
Fullerene Molecule ◽  
Graph Labeling ◽  
Fullerene Graph ◽  
Theoretical Concepts ◽  
Large Numbers ◽  
Fullerene Graphs

Aims and Objective: A fullerene graph is a mathematical model of a fullerene molecule. A fullerene molecule or simply a fullerene is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Chemical graph theory is a combination of chemistry and graph theory where graph theoretical concepts used to study physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory which has application not only within mathematics but also in computer science, coding theory, medicine, communication networking, chemistry and in many other fields. For example, in chemistry vertex labeling is being used in the constitution of valence isomers and transition labeling to study chemical reaction networks. Method and Results: In terms of graphs vertices represent atoms while edges stand for bonds between atoms. By tvs (tes) we mean the least positive integer for which a graph has a vertex (edge) irregular total labeling such that no two vertices (edges) have same weights. A (3,6)-fullerene graph is a non-classical fullerene whose faces are triangles and hexagons. Here, we study the total vertex (edge) irregularity strength of an arbitrary disjoint union of (3,6)-fullerene graphs and providing their exact values. Conclusion: The lower bound for tvs (tes) depending on the number of vertices, minimum and maximum degree of a graph exists in literature while to get different weights one can use sufficiently large numbers, but it is of no interest. Here, by proving that the lower bound is the upper bound we close the case for (3,6)-fullerene graphs.

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