Elements of Graph Theory I. The Definition of a Graph

2018 ◽  
pp. 25-44
Keyword(s):  
Graph Theory ◽  
Definition Of

scholarly journals Medicinal cupping in the eyes of graph theory

2020 ◽  
Vol 1 (01) ◽  
pp. 44-49
Author(s):  
N.M Hanafi ◽  
Y. Yusof ◽  
M.S. Mohamad ◽  
M.F.A Bakar ◽  
M.A. Ibrahim
Keyword(s):  
Graph Theory ◽  
Human Health ◽  
Healing Process ◽  
Optimal Number ◽  
Simple Graph ◽  
The Body ◽  
Graph Colouring ◽  
Traditional Treatment ◽  
The World ◽  
Definition Of

Medicinal cupping is one of the traditional treatment methods that is trusted to give many benefits to the human health and still practising by various culture and societies around the world. The purposes of this treatment are to allow the toxin leaves the body,to stimulate the muscles and also helping in healing process for various diseases. The process start by placing special heated cups on specific points to create suction, then the points will be punctured. Each disease has specific cupping points to be cupped which located on the human nerves system. All the points actually connected to each other where a simple graph can be formed. Since there are limited studies that discuss medicinal cupping in a mathematics view, thus this research is conducted to introduce the easiest way  on demonstrating the cupping points on the human nerves system by using the idea of graph. Hence, new definition of nerve vertex, nerve edge and nerve graph will be defined. Moreover, the idea of graph colouring will be applied to determine the optimal number of cupping points.

scholarly journals A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 551 ◽  
Author(s):  
Liangsong Huang ◽  
Yu Hu ◽  
Yuxia Li ◽  
P. K. Kishore Kumar ◽  
Dipak Koley ◽  
...  
Keyword(s):  
Graph Theory ◽  
Optimization Problems ◽  
Real Life ◽  
Road Transport ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Real World Problem ◽  
Neutrosophic Graph ◽  
Definition Of

Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

Analysis on Degree of Freedom and Singularity of Mechanism Based on Topological Graph Theory

2011 ◽  
Vol 393-395 ◽  
pp. 20-23
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Graph Theory ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Graph ◽  
Topological Graph Theory ◽  
Hybrid Mechanism ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Case Number

Based on the analysis of current developing state of graph theory, define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the new description method in topological graph theory. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented, as well as the necessary and sufficient condition of singularity of mechanism deduced , in-phase and assimilation condition and in-phase and dissimilarity condition and asynchronism condition of limitation of input base of branch adopted, case number of position singularity and pose singularity and position and pose singularity obtained then, still the way of founding the combination and case number of common serial mechanism and parallel mechanism and hybrid mechanism mentioned.

Research on Tool Flow Deadlock Based on Petri Net and Graph Theory

2010 ◽  
Vol 450 ◽  
pp. 59-62
Author(s):  
Dan Zhao ◽  
Shao Gang Liu ◽  
Hai Sheng Shu
Keyword(s):  
Graph Theory ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Manufacturing System ◽  
Sufficient Conditions ◽  
Machine Process ◽  
The Past ◽  
Set Up ◽  
Definition Of ◽  
Necessary And Sufficient

Part flow and tool flow were the two mainly aspects of the workflow in flexible manufacturing system. During the past decades part flow deadlock was much more considered than that of tool flow. Tool flow deadlock problem in the condition that the production procedure can be interrupted was studied in this paper. The model of machine process based on the Petri net was set up and the definition of tool flow deadlock was proposed. Necessary and sufficient conditions for deadlock and potential deadlock were discussed according to graph theory method. A case was illustrated and showed that this method was to be correct and effective.

ADAPTIVE K-MEANS ALGORITHM FOR OVERLAPPED GRAPH CLUSTERING

2012 ◽  
Vol 22 (05) ◽  
pp. 1250018 ◽  
Author(s):  
GEMA BELLO-ORGAZ ◽  
HÉCTOR D. MENÉNDEZ ◽  
DAVID CAMACHO
Keyword(s):  
Genetic Algorithm ◽  
Social Networks ◽  
Graph Theory ◽  
Clustering Algorithms ◽  
Graph Clustering ◽  
Clustering Problem ◽  
Fitness Functions ◽  
Automatic Adaptation ◽  
Clustering Approach ◽  
Definition Of

The graph clustering problem has become highly relevant due to the growing interest of several research communities in social networks and their possible applications. Overlapped graph clustering algorithms try to find subsets of nodes that can belong to different clusters. In social network-based applications it is quite usual for a node of the network to belong to different groups, or communities, in the graph. Therefore, algorithms trying to discover, or analyze, the behavior of these networks needed to handle this feature, detecting and identifying the overlapped nodes. This paper shows a soft clustering approach based on a genetic algorithm where a new encoding is designed to achieve two main goals: first, the automatic adaptation of the number of communities that can be detected and second, the definition of several fitness functions that guide the searching process using some measures extracted from graph theory. Finally, our approach has been experimentally tested using the Eurovision contest dataset, a well-known social-based data network, to show how overlapped communities can be found using our method.

Computing the Theta Polynomial Θ(G, x) and the Theta Index Θ(G) of Titania Nanotubes TiO2(m, n)

2017 ◽  
Vol 14 (1) ◽  
pp. 715-717
Author(s):  
Yingfang Li ◽  
Li Yan ◽  
Mohammad R Farahani ◽  
Muhammad Imran ◽  
Muhammad K Jamil
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Infinite Family ◽  
Titania Nanotubes ◽  
Chemical Graph ◽  
First Derivative ◽  
Chemical Graph Theory ◽  
Omega Polynomial ◽  
Definition Of ◽  
First Time

Let G = (V,E) be a simple connected molecular graph in chemical graph theory, where the vertex/atom set and edge/bond set of G denoted by V(G) and E(G), respectively and its vertices correspond to the atoms and the edges correspond to the bonds. Two counting polynomials the “Omega Ω(G,x) and Theta Θ(G,x)” polynomials of a molecular graph G were defined by Diudea as Ω(G,x) = ΣeE(G) xn(E) and Θ(G,x) = ΣeE(G) xn(E), where n(E) denotes the number of edges co-distant with the edge E. From definition of these counting polynomials, we can obtain the Theta polynomial by inserting the coefficient n(E) in the Omega polynomial. Then the Theta index will be the first derivative of the Theta polynomial Θ(G,x) evaluated at x = 1. The goal of this paper is to compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of an infinite family of the Titania Nanotubes TiO2(m,n) for the first time.

scholarly journals Analysis of Internal and External Academic Collaboration in an Institution Through Graph Theory

2020 ◽  
Vol 07 (04) ◽  
pp. 391-415
Author(s):  
Jared D. T. Guerrero-Sosa ◽  
Víctor H. Menéndez-Domínguez ◽  
María-Enriqueta Castellanos-Bolaños ◽  
Luis F. Curi-Quintal
Keyword(s):  
Data Mining ◽  
Graph Theory ◽  
Scientific Collaboration ◽  
State Of The Art ◽  
Collaborative Work ◽  
Open Science ◽  
Research Groups ◽  
Digital Repositories ◽  
Definition Of ◽  
Theory Of Graphs

This paper presents an analysis of scientific collaboration through graph theory, based on a previous study focused on the collaborative work of researchers within an institution. This proposal also exposes the representation of inter-institutional collaboration of research groups, combining graph theory and data mining. The state of the art relates the concepts of scientific production, digital repositories, interoperability between repositories, the law of Open Science in Mexico, the theory of graphs and their use in previous studies for the analysis of scientific collaboration, and the definition of research groups in Mexico. Furthermore, the methodology uses elements of knowledge extraction for data mining, involving recovery, processing and visualization. Results present the collaboration status at the Universidad Autónoma de Yucatán, internally and externally, by the research groups. Internally, 22 groups were found and each researcher collaborates with six other professors within the institution, on average. In addition, consolidated research groups are those with the highest level of production and collaboration at national and international level, compared to the groups with less consolidation.

Analysis on Degree of Freedom and Singularity of Mechanism Based on Topological Graph Theory

2012 ◽  
Vol 430-432 ◽  
pp. 1943-1946
Author(s):  
Jian Guo Luo ◽  
Mao Yan He
Keyword(s):  
Graph Theory ◽  
Degree Of Freedom ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Graph ◽  
Topological Graph Theory ◽  
Hybrid Mechanism ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Case Number

Based on the analysis of current developing state of graph theory, define the description of spacial moving capability of common couples and translation base and rotation base of mechanism, based on the new description method in topological graph theory. DOF(degree of freedom) of hybrid mechanism analysised with example based on the definition of dimensionity of branch spacial moving capability and mechanism spacial moving capability, necessary and sufficient condition of nonsingularity of mechanism presented, as well as the necessary and sufficient condition of singularity of mechanism deduced , in-phase and assimilation condition and in-phase and dissimilarity condition and asynchronism condition of limitation of input base of branch adopted, case number of position singularity and pose singularity and position and pose singularity obtained then, still the way of founding the combination and case number of common serial mechanism and parallel mechanism and hybrid mechanism mentioned.

DISTANCE IN ZIGZAG POLYHEX NANOTORUS

2008 ◽  
Vol 07 (05) ◽  
pp. 1029-1039
Author(s):  
MEHDI ELIASI ◽  
BIJAN TAERI
Keyword(s):  
Biological Activity ◽  
Graph Theory ◽  
Physicochemical Properties ◽  
Chemical Structure ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Definition Of

Graph theory was successfully applied in developing a relationship between chemical structure and biological activity. The concept of distance in graphs is basic in the definition of various topological indices for chemical compounds, which determines some of the physicochemical properties of them. In this paper, we explain a method, using the concept of distance in the graph of zigzag polyhex nanotorus, which enables us to compute different topological indices simultaneously.

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