Advertisement

Dominating Laplacian Energy in Products of Intuitionistic Fuzzy Graphs

  • R. Vijayaragavan
  • A. Kalimulla
  • S. Sharief BashaEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The Laplacian energy of an intuitionistic fuzzy graph concept is extended to dominating Laplacian energy in various products of intuitionistic fuzzy graph. In this paper, we have obtained the value of dominating Laplacian energy in two products such as Cartesian product and tensor product. Also we study the relation between the dominating Laplacian energy in the products in two intuitionistic fuzzy graphs.

References

  1. 1.
    Atanassov, K.: Intuitionistic Fuzzy sets : Theory and Applications, Springer-Verlag, Heidelberg, (1999).CrossRefGoogle Scholar
  2. 2.
    Gutman,I.: Gutman,I. The Energy of a Graph, Ber. Math - Statist. Sekt. Forschungsz. Graz, 103, 1–22 , (1978).Google Scholar
  3. 3.
    Nagoorgani.A and Chandrasekaran.V.T, Domination in Fuzzy Graph, Advances in Fuzzy Sets and systems, 1(1),17–26 (2006).Google Scholar
  4. 4.
    Parvathi R, Karumbigai M G. Intutionistic fuzzy graphs. Computational Intelligence, Theory and Applications. 139–150.Google Scholar
  5. 5.
    Parvathi R and G. Thamizhendhi, Domination in intuitionistic fuzzy graphs, Fourteenth Int. Conf. on IFSs, Sofia, 15–16 May 2010 ,NIFS Vol. 16 (2010), 2, 39–49.Google Scholar
  6. 6.
    Parvathi R and G. Thamizhendhi, Some results on domination number in products of intuitionistic fuzzy graphs, , Annals of Fuzzy mathematics and Informatics,September 2014, Vol:10 , SNo:10 , pp:1–20.Google Scholar
  7. 7.
    Rosenfeld.A, Fuzzy Graphs, in Zadeh.L.A, Fu. K.cS, Tanaka.K and Shimura.M (eds.),Google Scholar
  8. 8.
    Somasundaram.A and Somasundaram.S, Domination in Fuzzy Graphs – I, Elsevier Science, 19, 787–791 (1998).Google Scholar
  9. 9.
    Sharief Basha.S and E. Kartheek, Laplacian Energy of an Intuitionistic Fuzzy Graph, Indian Journal of Science and Technology, ,Vol 8(33),1–7 , (Dec2015).Google Scholar
  10. 10.
    R.Vijayaragavan , A.Kalimulla , S. Sharief Basha, Dominating Energy in Products of intuitionistic Fuzzy Graphs, Journal of Global Pharma Technology, 2017; 06(9):58–71.Google Scholar
  11. 11.
    Zadeh.L.A., Fuzzy sets , Information and Control, 1965;, 8: 338–353.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • R. Vijayaragavan
    • 1
  • A. Kalimulla
    • 2
  • S. Sharief Basha
    • 3
    Email author
  1. 1.Department of MathematicsThiruvalluvar UniversitySerkadu, VelloreIndia
  2. 2.Thiruvalluvar UniversitySerkadu, VelloreIndia
  3. 3.Applied Algebra Division, School of Advanced SciencesVIT UniversityVelloreIndia

Personalised recommendations