Applied Mathematics and Scientific Computing pp 507-515 | Cite as
Location-2-Domination for Product of Graphs
Conference paper
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Abstract
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.
Keywords
Cartesian product of graphs Direct product of graphs Domination number Location-2-domination numberReferences
- 1.Faudree, R.J., Schelp, R.H.: The domination number for the product of graphs. Congr. Numer., 79, 29–33 (1990).MathSciNetzbMATHGoogle Scholar
- 2.Harary, F., Haynes, T.W.: Double domination in graphs. Ars Combin., 55, 201–213 (2000).MathSciNetzbMATHGoogle Scholar
- 3.Haray, F.: Graph theory, Addison Wesley, Reading MA, 1969.CrossRefGoogle Scholar
- 4.Haynes, T.W., Hedetniemi, S.T., Salter. P.J.: Fundamentals of domination in graphs, Marcel Decker, Inc., New York, 1997Google Scholar
- 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.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.Slater, P.J.: Dominating and reference sets in a graph. J. Math. Phys. Sci., 22 (1988), 445–455.MathSciNetzbMATHGoogle Scholar
- 8.Slater, P.J.: Domination and location in acyclic graphs. Wiley online library, 55–64 (1987) https://onlinelibrary.wiley.com/.MathSciNetCrossRefGoogle Scholar
- 9.Sitthiwirattham, T.: Domination on Kronecker product of P n. Applied Mathematical Sciences, 6, No. 87, 4345–4352 (2012).MathSciNetzbMATHGoogle Scholar
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