scholarly journals Novel Concepts of Domination in Vague Graphs with Application in Medicine

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiaoli Qiang ◽  
Maryam Akhoundi ◽  
Zheng Kou ◽  
Xinyue Liu ◽  
Saeed Kosari
Keyword(s):  
Biological Networks ◽  
Coding Theory ◽  
Location Problem ◽  
Dominating Set ◽  
Medical Science ◽  
Facility Location Problem ◽  
School Bus ◽  
Bus Routing ◽  
Wide Range ◽  
Real World Problems

VG can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. The previous definitions’ restrictions in FGs have made us present new definitions in VGs. A wide range of applications have been attributed to the domination in graph theory for several fields such as facility location problem, school bus routing, modeling biological networks, and coding theory. Therefore, in this research, we study several concepts of domination, such as restrained dominating set (RDS), perfect dominating set (PDS), global restrained dominating set (GRDS), total k -dominating set, and equitable dominating set (EDS) in VGs and also introduce their properties by some examples. Finally, we try to represent the application and importance of domination in the field of medical science and discuss the topic in today’s world, namely, the corona vaccine.

scholarly journals Equitable Domination in Vague Graphs With Application in Medical Sciences

2021 ◽  
Vol 9 ◽  
Author(s):  
Yongsheng Rao ◽  
Saeed Kosari ◽  
Zehui Shao ◽  
Xiaoli Qiang ◽  
Maryam Akhoundi ◽  
...  
Keyword(s):  
Biological Networks ◽  
Coding Theory ◽  
Social Systems ◽  
Medical Science ◽  
Real Life ◽  
Electrical Networks ◽  
Dominating Sets ◽  
Medical Sciences ◽  
Height Measurement ◽  
Wide Range

Considering all physical, biological, and social systems, fuzzy graph (FG) models serve the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problem, which is mostly uncertain, modeling the problems based on FGs is highly demanding for an expert. Vague graphs (VGs) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. In addition, VGs are a very useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, medical science, and traffic plan. The previous definition restrictions in FGs have made us present new definitions in VGs. A wide range of applications has been attributed to the domination in graph theory for several fields such as facility location problems, school bus routing, modeling biological networks, and coding theory. Concepts from domination also exist in problems involving finding the set of representatives, in monitoring communication and electrical networks, and in land surveying (e.g., minimizing the number of places a surveyor must stand in order to take the height measurement for an entire region). Hence, in this article, we introduce different concepts of dominating, equitable dominating, total equitable dominating, weak (strong) equitable dominating, equitable independent, and perfect dominating sets in VGs and also investigate their properties by some examples. Finally, we present an application in medical sciences to show the importance of domination in VGs.

Comperehencive review of Tankana

2018 ◽  
Vol 3 (4) ◽  
Author(s):  
Dr. Jyotsna Sankpal ◽  
Dr. Jyotsna Takalikar
Keyword(s):  
Heart Disease ◽  
Medical Science ◽  
Menstrual Disorders ◽  
Therapeutic Applications ◽  
Indian Medical ◽  
Wide Range ◽  
Long Time

Rasa Shastra and Bhaishajya Kalpana is branch of the ancient Indian medical science based on herbs and herbo-mineral preparation. Tankana has been described under Uparasa Tankana, which is one among the Kshara Trayas has been used since very long time in Ayurveda. It has a wide range of therapeutic applications, including diseases like Varna (ulcers), Shvasa (asthma), Kasa (cough), Hrudya (beneficial to heart disease), Streepushpajanana (menstrual disorders) etc. It is used in the form of compound formulations like Parpati, Kupipakwa, Khalvee Rasayana, Churna, Vati, Lepa etc. In this paper Tankana Shodhana procedure, different synonyms, dose, Anupana, indications and different formulations containing Tankana Bhasma has been discussed.

scholarly journals Dispersing Obnoxious Facilities on a Graph

Algorithmica ◽  
2021 ◽  
Author(s):  
Alexander Grigoriev ◽  
Tim A. Hartmann ◽  
Stefan Lendl ◽  
Gerhard J. Woeginger
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Unit Length ◽  
Facility Location Problem ◽  
Np Hard ◽  
Obnoxious Facilities ◽  
Rational Parameter ◽  
Polynomially Solvable

AbstractWe study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance $$\delta$$ δ from each other. We investigate the complexity of this problem in terms of the rational parameter $$\delta$$ δ . The problem is polynomially solvable, if the numerator of $$\delta$$ δ is 1 or 2, while all other cases turn out to be NP-hard.

Fuzzy facility location problem with preference of candidate sites

2007 ◽  
Vol 158 (17) ◽  
pp. 1922-1930 ◽  
Author(s):  
Hiroaki Ishii ◽  
Yung Lung Lee ◽  
Kuang Yih Yeh
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem
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