Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Strengthening and Weakening Members of a Network Read chapter Read first chapter

2018 | OriginalPaper | Chapter

2. Domination in Fuzzy Graphs

Authors : John N. Mordeson, Sunil Mathew, Davender S. Malik

Published in: Fuzzy Graph Theory with Applications to Human Trafficking

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The results of the next two sections are based on Somasundaram, Somasundaram (Pattern Recongit Lett 19:787–791, 1998), [29]. The formal mathematical definition of domination was given by Ore, (Theory of graphs. American Mathematical Society, Providence, 1962), [22]. Cockayne and Hedetnieme, (Networks 7:247–261, 1977, [3]), published a survey paper on this topic in 1977 and since then hundreds of papers have been published on this subject. According to Somasundaram, Somasundaram (Pattern Recongit Lett 19:787–791, 1998, [29]), the rapid growth of research in this area is due to the following three factors. (1) The diversity of applications of domination theory to both real world and mathematical coverings or location problems. (2) The wide variety of domination parameters that can be defined. (3) The NP-completeness of the basic domination problem, its close and natural relationship to other NP-complete problems and the subsequent interest in finding polynomial time solutions to domination problems in special classes of graphs.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Strengthening and Weakening Members of a Network
next chapter Fuzzy Incidence Graphs
Literature
1.
O. Bobrowicz, C. Choulet, A. Haurat, F. Sandoz, M. Tebaa (1990) A method to build membership functions — Application to numerical/symbolic interface building, in Proceedings of 3rd Internat. Conference on Information Processing and Management of Uncertainty in Knowledge Based System, Paris
2.
J.A. Bordy, U.S.R. Murty, Graph Theory with Applications, 5th edn. (MacMillan Press, New York, 1982)
3.
4.
E.J. Cockayne, O. Favaron, C. Payan, A.G. Thomason, Contribution to the theory of domination, independence, and irredundance in graphs. Discret. Math. 33, 249–258 (1981)MathSciNetCrossRefMATH
5.
F. Harary, Graph Theory, 3rd edn. (Addison Wesley, Reading, MA, 1972)MATH
6.
O.T. Manjusha, M.S. Sunitha, Notes on domination in fuzzy graphs. J. Intell. Fuzzy Syst. 27, 3205–3212 (2014)MathSciNetMATH
7.
O.T. Manjusha, M.S. Sunitha, Total domination in fuzzy graphs using strong arcs. Ann. Pure Appl. Math. 9(1), 23–33 (2014). ISSN: 2279-087X (P), 2279-0888MATH
8.
S. Mathew, J.N. Mordeson, Directed fuzzy networks and max-flow min cut theorem. New Math. Nat. Comput. 13, 219–229 (2017)MathSciNetCrossRef
9.
J.N. Mordeson, S. Mathew, Non determinisitc flow in networks and its application in identification of human trafficking chains. New Math. Nat. Comput. 13, 231–243 (2017)MathSciNetCrossRef
10.
A. Nagoor Gani and P. Veldivel, On irredundance in fuzzy graphs, Proceedings of the national Conference on Fuzzy Mathematics and Graph Theory, Jamal Mohamed College, Tiruchirappalli, March 2008, 40–43
11.
A. Nagoor Gani, V.T. Chandrasekaran, Domination in fuzzy graphs. Adv. Fuzzy Sets Syst. 1, 17–26 (2006)MathSciNet
12.
A. Nagoor Gani, P. Vadiel, A study on domination, independent domination, and irredundance in fuzzy graphs. Appl. Math. Sci. 5, 2317–2325 (2011)MathSciNetMATH
13.
A. Nagoor Gani, P. Veldivel, Relation between the parameters of independent domination and irredundance in fuzzy graph. Int. J. Algorithms Comput. Math. 2(1), 787–791 (1998)
14.
A. Nagoor Gani, P. Veldivel, Fuzzy independent dominating set. Adv. Fuzzy Sets Syst. 2(1), 99–108 (2007)MathSciNet
15.
A. Nagoor Gani, P. Veldivel, On domination, independence, and irredundance in fuzzy graphs. Int. Rev. Fuzzy Math. 3(2), 191–198 (2008)
16.
A. Nagoor Gani, P. Veldivel, Contribution to the theory of domination, independence, and irredundance in fuzzy graphs. Bull. Pure Appl. Sci. 28E(2), 179–187 (2009)MathSciNet
17.
A. Nagoor Gani, P. Veldivel, On the sum of the cardinality of independent and independent dominating \(S\) sets in fuzzy graph. Adv. Fuzzy Sets Syst. 4(2), 157–165 (2009)MathSciNetMATH
18.
A. Nagoor Gani, P. Vijayalakshmi, Domination critical nodes in fuzzy graphs. Int. J. Math. Sci. Eng. Appl. (IJMSEA) 5(1), 295–301 (2011)MathSciNet
19.
A. Nagoor Gani, P. Vijayalakshmi, Intensive arcs in domination of fuzzy graphs, Int. J. Contemp. Math Sci. 6(26), 1303–1309 (2011)MathSciNetMATH
20.
A. Nagoor Gani, P. Vijayalakshmi, Fuzzy graphs with equal fuzzy domination and independent domination numbers. Int. J. Eng. Sci. Technol. Dev. 1(2), 66–68 (2012)
21.
A. Nagor Gani, M. Basheer Ahamed, Strong and weak domination in fuzzy graphs. East Asian Math. J. 23, 1–8 (2007)MATH
22.
O. Ore, Theory of Graphs, vol. 38, American Mathematical Society Colloquium Publications (Americal Mathematical Society, Providence, RI, 1962)MATH
23.
S.S. Rajaram, S. Tidball, Nebraska Sex Trafficking Survivors Speak - A Qualitative Research Study, Submitted to the Women’s Fund of Omaha (2016)
24.
M. Reha Civanlar, H. Joel Trussel, Constructing membership functions using statistical data. Fuzzy Sets Syst. 18, 1–13 (1986)MathSciNetCrossRef
25.
I.C. Ross, F. Harary, Identification of strengthening and weakening members of a group. Sociometry 22, 139–147 (1959)MathSciNetCrossRef
26.
A. Somasundaram, S. Somasundaram, Domination in fuzzy graphs-I, Elsevier Science, 19, 787–791. Discrete Mathematics 33(1981), 249–258 (1998)
27.
28.
29.
A. Somasundaram, S. Somasundaram, Domination in fuzzy graphs-I. Pattern Recongit. Lett. 19, 787–791 (1998)CrossRefMATH
30.
E. Takeda, T. Nishida, An application of fuzzy graphs to the problem of group structure. J. Op. Res. Soc. Jpn. 19, 217–227 (1976)MathSciNetMATH
31.
United Nations Office on Drugs and Crime (UNODC) Trafficking in Persons Global Patterns (2006)
32.
United Nations Office on Drugs and Crime, Global Report on Trafficking in Persons (2014)
Metadata
Title
Domination in Fuzzy Graphs
Authors
John N. Mordeson
Sunil Mathew
Davender S. Malik
Copyright Year
2018
Book
Fuzzy Graph Theory with Applications to Human Trafficking

Print ISBN: 978-3-319-76453-5

Electronic ISBN: 978-3-319-76454-2

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-76454-2_2

Premium Partner

    Image Credits