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Yıl 2019, Cilt: 9 Sayı: 4, 800 - 809, 01.12.2019

Öz

Kaynakça

  • Breˇsar, B., Klavˇzar, S. and Rall, D. F., (2007), Dominating direct products of graphs, Discrete Math- ematics, 307(13), pp. 1636-1642.
  • Cockayne, E. J. and Hedetniemi, S. T., (1977), Towards a theory of domination in graphs, Networks, 7(3), pp. 247-261.
  • Kavaturi, V.S.R. and Vangipuram, S., (2016), The annihilator domination in some standard graphs and arithmetic graphs, International Journal of Pure and Applied Mathematics, 106(8), pp. 123-135.
  • Klavˇzar, S. and Zmazek, B., (1996), On a Vizing-like conjecture for direct product graphs, Discrete Mathematics, 156(1-3), pp. 243-246.
  • Kulli, V. R. and Janakiram, B., (1997), The split domination number of a graph, Graph theory notes of New York, 32(3), pp. 16-19.
  • Laskar, R. and Walikar, H. B., (1981), On domination related concepts in graph theory, Combinatorics and Graph Theory. Springer, Berlin, Heidelberg, pp. 308-320.
  • Sampathkumar, E., (1975), On tensor product graphs, Journal of the Australian Mathematical Society, 20(3), pp. 268-273.

ANNIHILATOR DOMINATION NUMBER OF TENSOR PRODUCT OF PATH GRAPHS

Yıl 2019, Cilt: 9 Sayı: 4, 800 - 809, 01.12.2019

Öz

An annihilator dominating set ADS is a representative technique for nd-ing the induced subgraph of a graph which can help to isolate the vertices. A dominating set of graph G is called ADS if its induced subgraph is containing only isolated vertices. The annihilator domination number of G, denoted by a G is the minimum cardinality of ADS. The tensor product of graphs G and H signi ed by G  H is a graph with vertex set V = V G V H and edge f u; v ; u0; v0 g 2 E whenever u; u0 2 E G and v; v0 2 E H . In this paper, we deduce exact values of annihilator domination number of tensor product of Pm and Pn, m; n 2. Further, we investigated some lower and upper bounds for annihilator domination number of tensor product of path graphs.

Kaynakça

  • Breˇsar, B., Klavˇzar, S. and Rall, D. F., (2007), Dominating direct products of graphs, Discrete Math- ematics, 307(13), pp. 1636-1642.
  • Cockayne, E. J. and Hedetniemi, S. T., (1977), Towards a theory of domination in graphs, Networks, 7(3), pp. 247-261.
  • Kavaturi, V.S.R. and Vangipuram, S., (2016), The annihilator domination in some standard graphs and arithmetic graphs, International Journal of Pure and Applied Mathematics, 106(8), pp. 123-135.
  • Klavˇzar, S. and Zmazek, B., (1996), On a Vizing-like conjecture for direct product graphs, Discrete Mathematics, 156(1-3), pp. 243-246.
  • Kulli, V. R. and Janakiram, B., (1997), The split domination number of a graph, Graph theory notes of New York, 32(3), pp. 16-19.
  • Laskar, R. and Walikar, H. B., (1981), On domination related concepts in graph theory, Combinatorics and Graph Theory. Springer, Berlin, Heidelberg, pp. 308-320.
  • Sampathkumar, E., (1975), On tensor product graphs, Journal of the Australian Mathematical Society, 20(3), pp. 268-273.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

K. Sharma Bu kişi benim

U. Sharma Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 4

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