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 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.

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 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.

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.

A ZONAL ALGORITHM FOR CLUSTERING AN HOC NETWORKS

2003 ◽  
Vol 14 (02) ◽  
pp. 305-322 ◽  
Author(s):  
YUANZHU PETER CHEN ◽  
ARTHUR L. LIESTMAN
Keyword(s):  
Ad Hoc ◽  
Mobile Ad Hoc Network ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Dominating Sets ◽  
New Approach ◽  
Graph Domination ◽  
Np Complete ◽  
Hoc Networks ◽  
Weakly Connected Dominating Set

A Mobile Ad Hoc Network (MANET) is an infrastructureless wireless network that can support highly dynamic mobile units. The multi-hop feature of a MANET suggests the use of clustering to simplify routing. Graph domination can be used in defining clusters in MANETs. A variant of dominating set which is more suitable for clustering MANETs is the weakly-connected dominating set. A cluster is defined to be the set of vertices dominated by a particular vertex in the dominating set. As it is NP-complete to determine whether a given graph has a weakly-connected dominating set of a particular size, we present a zonal distributed algorithm for finding small weakly-connected dominating sets. In this new approach, we divide the graph into regions, construct a weakly-connected dominating set for each region, and make adjustments along the borders of the regions to produce a weakly-connected dominating set of the entire graph. We present experimental evidence that this zonal algorithm has similar performance to and provides better cluster connectivity than previous algorithms.

scholarly journals METRICS FOR PERFORMANCE EVALUATION OF SAFETY APPLICATIONS IN VEHICULAR AD HOC NETWORKS

Transport ◽  
2008 ◽  
Vol 23 (4) ◽  
pp. 291-298 ◽  
Author(s):  
Saleh Yousefi ◽  
Mahmood Fathy
Keyword(s):  
Performance Evaluation ◽  
Ad Hoc Network ◽  
Vehicular Ad Hoc Networks ◽  
Ad Hoc ◽  
Road Traffic ◽  
Real Life ◽  
Message Exchange ◽  
To Come ◽  
Hoc Networks ◽  
Safety Applications

In the recent years, direct message exchange between vehicles in order to improve the safety of road traffic has been attracting lots of interest in both networking and road safety communities. While travelling on a road, vehicles form an ad hoc network called Vehicular Ad hoc NETwork (VANET) and deploy life safety applications. Evaluating the performance of these applications is primordial for realizing VANETs in real life. Current literature lacks efficient ways to evaluate the performance of safety applications and mostly leverages on classical networking metrics like delay, delivery rate etc. In this paper, we consider both networking and safety concerns simultaneously to come up with more efficient methods. In particular, we first point out the significance of fairness and coverage from safety viewpoint. Then, we introduce two new metrics called beaconing rate and effective range aiming at providing more facilities for safety performance evaluation in VANET s research. Furthermore, realizing special characteristics of safety applications while disseminating beacon messages, we study the way that beacon dissemination protocols affect the performance of safety applications. We then conduct extensive simulation study to show the usefulness of the introduced metrics and derive some insights on the feasibility of driver‐assistant safety applications. Our evaluation also shows that sending the aggregated status of neighbouring vehicles in addition to vehicle's own status, and instead, increasing beacon transmission interval may be invoked in order to assist safety applications in providing satisfactory services to drivers.

scholarly journals The Use of Bluetooth Standard for Communication Between Vehicles Under Traffic

2018 ◽  
Vol 45 (1) ◽  
pp. 67-82
Author(s):  
Zbigniew Kasprzyk ◽  
Mariusz Rychlicki
Keyword(s):  
Ad Hoc Networks ◽  
Ad Hoc Network ◽  
Ad Hoc ◽  
Real Life ◽  
Radio Waves ◽  
Radio Communications ◽  
Audio Data ◽  
Close Range ◽  
Hoc Networks ◽  
Voice Data

Abstract Bluetooth is a type of wireless communication used to transmit voice and data at high speeds using radio waves. It is a standard protocol for short-range radio communications between many different types of devices, including mobile phones, computers and other electronics [1]. The use of this type of data transmission standard for voice communications at close range in the vehicle is commonly known. The trend of integrating new services in vehicles increases rapidly and Bluetooth is one of the emerging communication technologies for realizing ad-hoc networks. The paper presents the possibility of using Bluetooth to build ad-hoc network suitable for the transmission of sound, in particular voice data using the modulation GSFK. We analyzed the features or problems that Bluetooth offers for transmitting audio data in an ad-hoc network. Some initial results of simulations and real-life tests give an impression of the performance and efficiency this standard for the transmission of voice data in an ad-hoc networks [2].

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