scholarly journals A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1885
Author(s):  
Yongsheng Rao ◽  
Saeed Kosari ◽  
Zehui Shao ◽  
Ruiqi Cai ◽  
Liu Xinyue
Keyword(s):  
Mobile Networks ◽  
Real World ◽  
Ad Hoc ◽  
Dominating Set ◽  
Real Life ◽  
Practical Interest ◽  
Dominating Sets ◽  
Medical Sciences ◽  
Incidence Graph ◽  
Vague Data

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been acknowledged as being an applicable and well-organized tool to epitomize and solve many multifarious real-world problems in which vague data and information are essential. Owing to unpredictable and unspecified information being an integral component in real-life problems that are often uncertain, it is highly challenging for an expert to illustrate those problems through a fuzzy graph. Therefore, resolving the uncertainty accompanying the unpredictable and unspecified information of any real-world problem can be done by applying a vague incidence graph (VIG), based on which the FGs may not engender satisfactory results. Similarly, VIGs are outstandingly practical tools for analyzing different computer science domains such as networking, clustering, and also other issues such as medical sciences, and traffic planning. Dominating sets (DSs) enjoy practical interest in several areas. In wireless networking, DSs are being used to find efficient routes with ad-hoc mobile networks. They have also been employed in document summarization, and in secure systems designs for electrical grids; consequently, in this paper, we extend the concept of the FIG to the VIG, and show some of its important properties. In particular, we discuss the well-known problems of vague incidence dominating set, valid degree, isolated vertex, vague incidence irredundant set and their cardinalities related to the dominating, etc. Finally, a DS application for VIG to properly manage the COVID-19 testing facility is introduced.

scholarly journals Domination of Fuzzy Incidence Graphs with the Algorithm and Application for the Selection of a Medical Lab

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Irfan Nazeer ◽  
Tabasam Rashid ◽  
Juan Luis Garcia Guirao
Keyword(s):  
Mobile Networks ◽  
Ad Hoc ◽  
Dominating Set ◽  
Domination Number ◽  
Wireless Networking ◽  
Dominating Sets ◽  
Fuzzy Graphs ◽  
Vague Data ◽  
Selection Of ◽  
Real World Problems

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been recognized as being an effective tool to tackle real-world problems in which vague data and information are essential. Dominating sets (DSs) have multiple applications in diverse areas of life. In wireless networking, DSs are being used to find efficient routes with ad hoc mobile networks. In this paper, we extend the concept of domination of FGs to the FIGs and show some of their important properties. We propose the idea of order, size, and domination in FIGs. Two types of domination, namely, strong fuzzy incidence domination and weak fuzzy incidence domination, for FIGs are discussed. A relationship between strong fuzzy incidence domination and weak fuzzy incidence domination for complete fuzzy incidence graphs (CFIGs) is also introduced. An algorithm to find a fuzzy incidence dominating set (FIDS) and a fuzzy incidence domination number (FIDN) is discussed. Finally, an application of fuzzy incidence domination (FID) is provided to choose the best medical lab among different labs for the conduction of tests for the coronavirus.

Dominations in Neutrosophic Graphs

2020 ◽  
pp. 131-147
Author(s):  
Mullai Murugappan
Keyword(s):  
Ad Hoc ◽  
Dominating Set ◽  
Domination Number ◽  
Real Life ◽  
Telecommunication Networks ◽  
Scheduling Problems ◽  
Dominating Sets ◽  
Molecular Physics ◽  
Neutrosophic Graph ◽  
Hoc Networks

The aim of this chapter is to impart the importance of domination in various real-life situations when indeterminacy occurs. Domination in graph theory plays an important role in modeling and optimization of computer and telecommunication networks, transportation networks, ad hoc networks and scheduling problems, molecular physics, etc. Also, there are many applications of domination in fuzzy and intuitionistic fuzzy sets for solving problems in vague situations. Domination in neutrosophic graph is introduced in this chapter for handling the situations in case of indeterminacy. Dominating set, minimal dominating set, independent dominating set, and domination number in neutrosophic graph are determined. Some definitions, characterization of independent dominating sets, and theorems of neutrosophic graph are also developed in this chapter.

scholarly journals An Enhanced Hybrid Social Based Routing Algorithm for MANET-DTN

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Martin Matis ◽  
L’ubomír Doboš ◽  
Ján Papaj
Keyword(s):  
Mobile Networks ◽  
Ad Hoc ◽  
Routing Algorithm ◽  
Real Life ◽  
Optimal Solution ◽  
Dynamic Topology ◽  
Disaster Situation ◽  
Dynamic Source ◽  
Small Density ◽  
Hoc Networks

A new routing algorithm for mobile ad hoc networks is proposed in this paper: an Enhanced Hybrid Social Based Routing (HSBR) algorithm for MANET-DTN as optimal solution for well-connected multihop mobile networks (MANET) and/or worse connected MANET with small density of the nodes and/or due to mobility fragmented MANET into two or more subnetworks or islands. This proposed HSBR algorithm is fully decentralized combining main features of both Dynamic Source Routing (DSR) and Social Based Opportunistic Routing (SBOR) algorithms. The proposed scheme is simulated and evaluated by replaying real life traces which exhibit this highly dynamic topology. Evaluation of new proposed HSBR algorithm was made by comparison with DSR and SBOR. All methods were simulated with different levels of velocity. The results show that HSBR has the highest success of packet delivery, but with higher delay in comparison with DSR, and much lower in comparison with SBOR. Simulation results indicate that HSBR approach can be applicable in networks, where MANET or DTN solutions are separately useless or ineffective. This method provides delivery of the message in every possible situation in areas without infrastructure and can be used as backup method for disaster situation when infrastructure is destroyed.

scholarly journals Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1279
Author(s):  
Irfan Nazeer ◽  
Tabasam Rashid ◽  
Muhammad Tanveer Hussain ◽  
Juan Luis García Guirao
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Real Life ◽  
Trade Policies ◽  
Trading System ◽  
Incidence Graph ◽  
Fuzzy Graphs ◽  
Innovative Idea ◽  
Minimum Number ◽  
Ambiguous Data

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are M[γs(Cl(σ,ϕ,η))]=⌈l3⌉. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization.

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.

scholarly journals Backbones for military multilayer wireless ad hoc networks based on networks science concepts

2018 ◽  
Author(s):  
Δημήτριος Παπακώστας
Keyword(s):  
Ad Hoc Networks ◽  
Wireless Ad Hoc Networks ◽  
Ad Hoc ◽  
Dominating Set ◽  
Np Hard ◽  
Dominating Sets ◽  
Edge Dominating Set ◽  
Connected Node ◽  
Vehicle Ad Hoc Networks ◽  
Hoc Networks

Στο πλαίσιο της παρούσας διδακτορικής διατριβής εστιάζουμε στα στρατιωτικά πολυεπίπεδα ασύρματα δίκτυα και επενδύουμε στην τεχνολογία των ad hoc δικτύων προκειμένου να βελτιώσουμε την απόδοση τους. Οραματιζόμαστε τα Τακτικά ασύρματα δίκτυα να απαρτίζονται από στρώματα ad hoc δικτύων με κινούμενους κόμβους, τα οποία είναι αδιαφανώς συνδεδεμένα μεταξύ τους ως μέρος ενός απρόσκοπτου υπερδικτύου το οποίο επιτρέπει την άμεση ροή πληροφοριών μεταξύ των κόμβων του.Για την υλοποίηση αυτού του οράματος αρχικά βασιζόμαστε στη θεωρία των Connected node Dominating Sets (CDS) και προτείνουμε καινοτόμους αλγόριθμους οι οποίοι επιτυγχάνουν κατανεμημένα αποτελεσματική σύνδεση των ανωτέρω πολυεπίπεδων ad hoc δικτύων ώστε να μειωθεί η καθυστέρηση τους (latency), να βελτιωθεί η επεκτασιμότητά τους (scalability) και να αυξηθεί η διάρκεια της ζωής τους. Στη συνέχεια εξετάζουμε το πρόβλημα της αποτελεσματικής και ταυτόχρονα κατανεμημένης παρακολούθησης της διακίνησης δεδομένων εντός του πολυεπίπεδου ad hoc δικτύου. Ένα δύσκολο πρόβλημα, ιδιαίτερα αν αυτό πρόκειται να επιλυθεί μέσω της χρήσης κατανεμημένων αλγορίθμων, λόγω των προβλημάτων συντονισμού που έχουν να κάνουν με το πολυεπίπεδο περιβάλλον καθώς δύνανται να οδηγήσουν είτε σε απώλεια επικοινωνίας μεταξύ των επιπέδων του δικτύου είτε σε υπερβολική εξάρτηση αυτού από ένα συγκεκριμένο επίπεδό του. Για την επίλυση του συγκεκριμένου προβλήματος επενδύουμε στη θεωρία των Connected edge Dominating Sets (CEDS) και προτείνουμε νέους κατανεμημένους αλγορίθμους οι οποίοι υπολογίζουν για σκοπούς διαχείρισης ή/και παρακολούθησης του πολυεπίπεδου δικτύου μία επικάλυψη (overlay) αυτού η οποία εμπεριέχει μεγάλο αριθμό από διασυνδέσεις μεταξύ των επιπέδων του δικτύου έτσι ώστε η επικοινωνία μεταξύ αυτών να μη διακόπτεται εύκολα (είτε κατά λάθος είτε λόγω κακόβουλων επιθέσεων).Οι κύριες συνεισφορές της παρούσας διατριβής είναι: Παρουσιάζεται το πρόβλημα του υπολογισμού του (Minimum) Connected node Dominating Set (MCDS) σε πολυεπίπεδα δίκτυα το οποίο δεν έχει εξεταστεί μέχρι στιγμής στη βιβλιογραφία. Αποδεικνύουμε ότι, οι προσεγγίσεις είτε για επίλυση του συγκεκριμένου προβλήματος με βάση την αποσύνθεση του πολυεπίπεδου δικτύου στα επιμέρους επίπεδά του είτε για συσσωμάτωση των επιπέδων του ώστε αυτά επί της ουσίας να μην υφίστανται δε θα φέρουν το επιθυμητό αποτέλεσμα και τονίζουμε την ανάγκη για αξιολόγηση αλλά και περαιτέρω εκμετάλλευση των διασυνδέσεων που διαθέτουν οι κόμβοι του δικτύου ώστε αυτοί να θεωρηθούν ως υποψήφια μέλη του DS. Στο πλαίσιο αυτό, προτείνουμε μία ομάδα από μέτρα για τη μέτρηση της σημαντικότητας του κάθε κόμβου εντός του πολυεπίπεδου δικτύου ώστε να προσδιοριστεί η στρατηγική θέση καθενός από αυτούς. Επίσης, προτείνουμε αλγόριθμους οι οποίοι υπολογίζουν κατανεμημένα το επιζητούμενο MCDS και παρουσιάζουν ανώτερη απόδοση σε σύγκριση με άλλους ευρέως χρησιμοποιούμενους αλγόριθμους.Παρουσιάζεται επίσης, το πρόβλημα της εύρεσης (Minimum) Connected Edge Dominating Set (MCEDS) σε πολυεπίπεδα δίκτυα. Αποδεικνύουμε ότι, το συγκεκριμένο πρόβλημα είναι NP-hard και προτείνουμε μία τεχνική η οποία προσδίδει στους κόμβους του πολυεπίπεδου δικτύου αντίληψη αναφορικά με τη σπουδαιότητα των ακμών που ακουμπούν σε πάνω σε αυτούς. Επιπρόσθετα, προτείνουμε νέους ευριστικούς αλγόριθμους οι οποίοι υπολογίζουν κατανεμημένα το MCEDS. Προτείνεται επίσης, ένας καινοτόμος αλγόριθμος πρόβλεψης για χρήση στο περιβάλλον των Vehicle Ad hoc Networks (VANETs) ο οποίος με καθαρά κατανεμημένο τρόπο και λαμβάνοντας υπόψη του την ιστορία κίνησης ενός οχήματος πραγματοποιεί online ακριβείς προβλέψεις αναφορικά με τη μελλοντική τροχιά του. Η προτεινόμενη μέθοδος συγκρίνεται με αντίστοιχους, υψηλής ακρίβειας, αλγόριθμους πρόβλεψης και τα αποτελέσματα επιβεβαιώνουν την ανωτερότητα της.

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.

scholarly journals Wireless Sensor Networks Fault-Tolerance Based on Graph Domination with Parallel Scatter Search

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3509
Author(s):  
Abdel-Rahman Hedar ◽  
Shada N. Abdulaziz ◽  
Emad Mabrouk ◽  
Gamal A. El-Sayed
Keyword(s):  
Ad Hoc Networks ◽  
Ad Hoc ◽  
Search Algorithm ◽  
Dominating Set ◽  
Scatter Search ◽  
Wireless Sensor ◽  
Virtual Backbone ◽  
Dominating Sets ◽  
Wireless Nodes ◽  
Hoc Networks

In wireless sensor/ad hoc networks, all wireless nodes frequently flood the network channel by transmitting control messages causing “broadcast storm problem”. Thus, inspired by the physical backbone in wired networks, a Virtual Backbone (VB) in wireless sensor/ad hoc networks can help achieve efficient broadcasting. A well-known and well-researched approach for constructing virtual backbone is solving the Connected Dominating Set (CDS) problem. Furthermore, minimizing the size of the CDS is a significant research issue. We propose a new parallel scatter search algorithm with elite and featured cores for constructing a wireless sensor/ad hoc network virtual backbones based on finding minimum connected dominating sets of wireless nodes. Also, we addressed the problem of VB node/nodes failure by either deploying a previously computed VBs provided by the main pSSEF algorithm that does not contain the failed node/nodes, or by using our proposed FT-pSSEF algorithm repairing the broken VBs. Finally, as nodes in a VB incur extra load of communication and computation, this leads to faster power consumption compared to other nodes in the network. Consequently, we propose the virtual backbone scheduling algorithm SC-pSSEF which aims to find multiple VBs using the VBs provided by the pSSEF algorithm and switch between them periodically to prolong the network life time.

scholarly journals A Survey on Domination in Vague Graphs with Application in Transferring Cancer Patients between Countries

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1258
Author(s):  
Yongsheng Rao ◽  
Ruxian Chen ◽  
Pu Wu ◽  
Huiqin Jiang ◽  
Saeed Kosari
Keyword(s):  
Dominating Set ◽  
Sufficient Conditions ◽  
Real Life ◽  
Practical Interest ◽  
Independent Set ◽  
Fuzzy Graph ◽  
Edge Dominating Set ◽  
Fuzzy Graphs ◽  
Wide Range ◽  
Dominance Set

Many problems of practical interest can be modeled and solved by using fuzzy graph (FG) algorithms. In general, fuzzy graph theory has a wide range of application in various fields. Since indeterminate information is an essential real-life problem and is often uncertain, modeling these problems based on FG is highly demanding for an expert. A vague graph (VG) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems in which fuzzy graphs may not succeed in bringing about satisfactory results. Domination in FGs theory is one of the most widely used concepts in various sciences, including psychology, computer sciences, nervous systems, artificial intelligence, decision-making theory, etc. Many research studies today are trying to find other applications for domination in their field of interest. Hence, in this paper, we introduce different kinds of domination sets, such as the edge dominating set (EDS), the total edge dominating set (TEDS), the global dominating set (GDS), and the restrained dominating set (RDS), in product vague graphs (PVGs) and try to represent the properties of each by giving some examples. The relation between independent edge sets (IESs) and edge covering sets (ECSs) are established. Moreover, we derive the necessary and sufficient conditions for an edge dominating set to be minimal and show when a dominance set can be a global dominance set. Finally, we try to explain the relationship between a restrained dominating set and a restrained independent set with an example. Today, we see that there are still diseases that can only be treated in certain countries because they require a long treatment period with special medical devices. One of these diseases is leukemia, which severely affects the immune system and the body’s defenses, making it impossible for the patient to continue living a normal life. Therefore, in this paper, using a dominating set, we try to categorize countries that are in a more favorable position in terms of medical facilities, so that we can transfer the patients to a suitable hospital in the countries better suited in terms of both cost and distance.

Efficient Self-Stabilizing Algorithm for Independent Strong Dominating Sets in Arbitrary Graphs

2015 ◽  
Vol 26 (06) ◽  
pp. 751-768 ◽  
Author(s):  
Brahim Neggazi ◽  
Nabil Guellati ◽  
Mohammed Haddad ◽  
Hamamache Kheddouci
Keyword(s):  
Ad Hoc ◽  
Dominating Set ◽  
Node Degree ◽  
Network Clustering ◽  
Dominating Sets ◽  
Arbitrary Graph ◽  
Practical Applications ◽  
Independence Properties ◽  
Hoc Networks ◽  
Arbitrary Graphs

In computer networks area, the minimal dominating sets (MDS) and maximal independent sets (MIS) structures are very useful for creating virtual network overlays. Often, these set structures are used for designing efficient protocols in wireless sensor and ad-hoc networks. In this paper, we give a particular interest to one kind of these sets, called Independent Strong Dominating Set (ISD-set). In addition to its domination and independence properties, the ISD-set considers also node’s degrees that make it very useful in practical applications where nodes with larger degrees play important role in the networks. For example, some network clustering protocols chose nodes with large degrees to be cluster-heads, which is exactly the result obtained by an ISD-set algorithm. Thence, we propose the first distributed self-stabilizing algorithm for computing an ISD-set of an arbitrary graph (called ISDS). Then, we prove that ISDS algorithm operates under the unfair distributed scheduler and converges after at most [Formula: see text] rounds requiring only [Formula: see text] space memory per node where Δ is the maximum node degree. The complexity of ISDS algorithm in rounds has the same order as the best known self-stabilizing algorithms for finding MDS and MIS. Moreover, performed simulations and comparisons with well-known self-stabilizing algorithms for MDS and MIS problems showed the efficiency of ISDS, especially for reducing the cardinality of dominating sets founded by the algorithms.

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