scholarly journals Nikfar Domination Versus Others: Restriction, Extension Theorems and Monstrous Examples

2019 ◽  
Author(s):  
Mohammadesmail Nikfar
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Dynamic State ◽  
Fuzzy Graph ◽  
Transport Planning ◽  
Open Problems ◽  
Static State ◽  
Extension Theorems ◽  
Real World Problem ◽  
Expository Article

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. Domination can be seen as arising from real-world application and extracting classical results as first described by this article.The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

scholarly journals Nikfar Domination in Fuzzy Graphs

2019 ◽  
Author(s):  
Mohammadesmail Nikfar
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Dynamic State ◽  
Fuzzy Graph ◽  
Transport Planning ◽  
Open Problems ◽  
Static State ◽  
Fuzzy Graphs ◽  
Real World Problem ◽  
Expository Article

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

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.

scholarly journals Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaolong Shi ◽  
Saeed Kosari
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Dominating Set ◽  
Independent Set ◽  
Fuzzy Graph ◽  
Medical Sciences ◽  
Total Dominating Set ◽  
Fuzzy Graphs ◽  
Vague Graph ◽  
Real World Problems

The product vague graph (PVG) is one of the most significant issues in fuzzy graph theory, which has many applications in the medical sciences today. The PVG can manage the uncertainty, connected to the unpredictable and unspecified data of all real-world problems, in which fuzzy graphs (FGs) will not conceivably ensue into generating adequate results. The limitations of previous definitions in FGs have led us to present new definitions in PVGs. Domination is one of the highly remarkable areas in fuzzy graph theory that have many applications in medical and computer sciences. Therefore, in this study, we introduce distinctive concepts and properties related to domination in product vague graphs such as the edge dominating set, total dominating set, perfect dominating set, global dominating set, and edge independent set, with some examples. Finally, we propose an implementation of the concept of a dominating set in medicine that is related to the COVID-19 pandemic.

Systems theories

2018 ◽  
Author(s):  
Marc J. Stern
Keyword(s):  
Social Networks ◽  
Problem Solving ◽  
Natural Resources ◽  
Real World ◽  
Common Pool Resources ◽  
Ecological Systems ◽  
Effective Governance ◽  
Social Ecological Systems ◽  
Social Ecological ◽  
Real World Problem

This chapter covers systems theories relevant to understanding and working to enhance the resilience of social-ecological systems. Social-ecological systems contain natural resources, users of those resources, and the interactions between each. The theories in the chapter share lessons about how to build effective governance structures for common pool resources, how to facilitate the spread of worthwhile ideas across social networks, and how to promote collaboration for greater collective impacts than any one organization alone could achieve. Each theory is summarized succinctly and followed by guidance on how to apply it to real world problem solving.

Fuzzy graph theory in coloring graph

2021 ◽  
Author(s):  
S. Sangeetha ◽  
P. Hema ◽  
N. Selvarani ◽  
P. Geetha ◽  
P. Karthikeyan ◽  
...  
Keyword(s):  
Graph Theory ◽  
Fuzzy Graph ◽  
Coloring Graph

Increase of energy efficiency ratio of a direct evaporative cooler by dynamic behavior with energy and exergy analysis

2021 ◽  
pp. 095440622110420
Author(s):  
Behzad Omidi Kashani
Keyword(s):  
Energy Efficiency ◽  
Electrical Energy ◽  
Coefficient Of Performance ◽  
Dynamic State ◽  
Circulation Rate ◽  
Cooling Load ◽  
Efficiency Ratio ◽  
Static State ◽  
Circulation Pump ◽  
Water Rate

The present research is about increasing the energy efficiency ratio (EER) in current direct evaporative coolers (DEC) in Iran. Increasing the cooling load and reducing the electrical energy consumption simultaneously (increasing the energy efficiency ratio (EER)) in DEC are the main goals of manufacturers and consumers of this device. When the circulation water pump runs continuously (static state), the circulation water rate is about 1.89 to 2.90 times of the amounts recommended in the reasonable standards. In order to adjust the circulation water rate to the recommended amount by standards, the present study has utilized repetitive cyclic scheduling programs to reduce the circulation rate to the optimal amount, (by turning the circulation pump on and off by dynamic pattern operation). In other words, the circulation pump stays on only for a certain period of a working cycle, and then the pump stays off for the rest of it. The cooling load and EER were measured based on ASHRAE 133 (2015). The results indicated that the cooling load in the dynamic state increased by 5.03 and 6.18 percent compared to the static state at low and high fan speeds, respectively. Moreover, in comparison with the static state, the amount of electrical energy consumed (kW-hr) in the dynamic state decreased by 8.8 and 4.2 percent at low and high fan speeds, respectively. Finally, the coefficient of performance (COP or EER) of the DEC in the dynamic state is increased by 15.16 and 10.78 in comparison with the static state at low and high fan speeds, respectively.

Effects of Additives in KOH Based Electrolytes on Cu ECMP

2007 ◽  
Vol 991 ◽  
Author(s):  
Tae-Young Kwon ◽  
In-Kwon Kim ◽  
Jin-Goo Park
Keyword(s):  
Citric Acid ◽  
Applied Voltage ◽  
Counter Electrode ◽  
Corrosion Potential ◽  
Removal Rate ◽  
Chemical Mechanical Planarization ◽  
Corrosion Current ◽  
Dynamic State ◽  
Static State ◽  
Potentiodynamic Curves

ABSTRACTThe purpose of this study was to characterize KOH based electrolytes and effects of additives on electro-chemical mechanical planarization. The electrochemical mechanical polisher was made to measure the potentiodynamic curve and removal rate of Cu. The potentiodynamic curves were measured in static and dynamic states in investigated electrolytes using a potentiostat. Cu disk of 2 inch was used as a working electrode and Pt electroplated platen was used as a counter electrode. KOH was used as the electrolyte. H2O2 and citric acid were used as additives for the ECMP of Cu. In static and dynamic potentiodynamic measurements, the corrosion potential decreased and corrosion current increased as a function of KOH concentration. In dynamic state, different potentiodynamic curve was obtained when compared to the static state. The current density did not decrease in passivation region by mechanical polishing effect. The static etch and removal rate were measured as function of KOH concentration and applied voltage. In ECMP system, polishing was performed at 30 rpm and 1 psi. The removal rate was about 60 nm/min at 0.3 V when 5 wt% KOH was used. Also, the effect of additive was investigated in KOH based electrolyte on removal rates. As a result, The removal rate was increased to 350 nm/min when 5wt% KOH, 5vol% H2O2, 0.3 M citric acid were used.

scholarly journals Preparing Biomedical Engineers For Real World Problem Solving

2020 ◽  
Author(s):  
David Kelso ◽  
John D. Enderle ◽  
Kristina Ropella
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Real World Problem

scholarly journals Applications of Fuzzy Graph Theory Portrayed in Various Fields

2021 ◽  
Author(s):  
Abdul Muneera ◽  
T. Nageswara Rao ◽  
R. V. N. Srinivasa ◽  
J. Venkateswara Rao
Keyword(s):  
Graph Theory ◽  
Wireless Sensor Network ◽  
Sensor Network ◽  
Material Science ◽  
Natural Sciences ◽  
Wireless Sensor ◽  
Fuzzy Graph ◽  
Ecological Conditions ◽  
Fuzzy Graphs ◽  
Remote System

Abstract The intend of the paper is to grant the centrality of fuzzy graph (f-graph) hypothetical ideas and the uses of dominations in fuzzy graphs to different genuine circumstances in the territories of science and designing. It is seen an eminent development because of various applications in PC and correspondence, biomedical, atomic material science and science, interpersonal organizations, natural sciences and in different various regions. Interpersonal organizations are the zones where countless individuals are associated. A wireless sensor Network (WSN) remote system which comprises of spatially circulated independent sensors to screen the physical or ecological conditions, for example, pressure, temperature, sound and so forth and to communicate their data through the remote system to a fundamental area. This paper gives an audit of the employments of Fuzzy Graph theory in different sorts of fields.

scholarly journals A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

2020 ◽  
pp. 76-86
Author(s):  
admin admin ◽  
◽  
◽  
◽  
Wenhui Bai ◽  
...  
Keyword(s):  
Decision Making ◽  
Graph Theory ◽  
Comparative Analysis ◽  
Fuzzy Graph ◽  
Neutrosophic Sets ◽  
Inconsistent Information ◽  
Operational Laws ◽  
Engineering Economy ◽  
Multi Attribute Decision Making

In most realistic situations, the theory and method of multi-attribute decision-making have been widely used in different fields, such as engineering, economy, management, military, and others. Although many studies in some extended fuzzy contexts have been explored with multi-attribute decision-making, it is widely recognized that single-valued neutrosophic sets can describe incomplete, indeterminate and inconsistent information more easier. In this paper, aiming at addressing multi-attribute decision-making problems with single-valued neutrosophic information, related models and multi-attribute decision-making approaches based on the fuzzy graph theory are studied. In specific, the notion of single-valued neutrosophic sets and graphs is firstly introduced together with several common operational laws. Then a multi-attribute decision making method based on single-valued neutrosophic graphs is established. Finally, an illustrative example and a comparative analysis are conducted to verify the feasibility and efficiency of the proposed method.

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