Location-2-Domination for Product of Graphs

  • G. Rajasekar
  • A. Venkatesan
  • J. Ravi Sankar
Conference paper
Part of the Trends in Mathematics book series (TM)


Locating-2-Dominating Set is denoted as \(R_{2}^{D}(G)\), and in this chapter the Location-2-domination number for direct and Cartesian product of graphs, namely \({{P}_{n}}\square {{P}_{m}}\), \({{P}_{n}}\square {{S}_{m}}\), \({{P}_{n}}\square {{W}_{m}}\), \({{C}_{n}}\square {{C}_{m}}\), Pn × Pm, Pn × Sm, Cn × Pm, Cn × Cm, are being found.


Cartesian product of graphs Direct product of graphs Domination number Location-2-domination number 


  1. 1.
    Faudree, R.J., Schelp, R.H.: The domination number for the product of graphs. Congr. Numer., 79, 29–33 (1990).MathSciNetzbMATHGoogle Scholar
  2. 2.
    Harary, F., Haynes, T.W.: Double domination in graphs. Ars Combin., 55, 201–213 (2000).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Haray, F.: Graph theory, Addison Wesley, Reading MA, 1969.CrossRefGoogle Scholar
  4. 4.
    Haynes, T.W., Hedetniemi, S.T., Salter. P.J.: Fundamentals of domination in graphs, Marcel Decker, Inc., New York, 1997Google Scholar
  5. 5.
    Rajasekar, G., Venkatesan, A.: Location-2-Domination for simple graphs. Global Journal of Pure and Applied Mathematics, 13, No:9, 5049–5057 (2017).Google Scholar
  6. 6.
    Rajasekar, G., Venkatesan, A.: Location-2-Domination for special kinds of simple graphs. International Journal of Pure and Applied Mathematics, 117, No:5 , 13–20 (2017).Google Scholar
  7. 7.
    Slater, P.J.: Dominating and reference sets in a graph. J. Math. Phys. Sci., 22 (1988), 445–455.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Slater, P.J.: Domination and location in acyclic graphs. Wiley online library, 55–64 (1987) Scholar
  9. 9.
    Sitthiwirattham, T.: Domination on Kronecker product of P n. Applied Mathematical Sciences, 6, No. 87, 4345–4352 (2012).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • G. Rajasekar
    • 1
  • A. Venkatesan
    • 2
  • J. Ravi Sankar
    • 3
  1. 1.Department of MathematicsJawahar Science CollegeNeyveliIndia
  2. 2.Department of MathematicsSt. Joseph’s College of Arts and Science College (Autonomous)CuddaloreIndia
  3. 3.Department of Mathematics, School of Advanced SciencesVellore Institute of TechnologyVelloreIndia

Personalised recommendations