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Year 2019, Volume 9, Issue 4, 800 - 809, 01.12.2019

Abstract

References

  • 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

Year 2019, Volume 9, Issue 4, 800 - 809, 01.12.2019

Abstract

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.

References

  • 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.

Details

Primary Language English
Journal Section Research Article
Authors

K. SHARMA This is me
Department of Mathematics and Statistics, Banasthali University, Banasthali (304022), India.


U. SHARMA This is me
Department of Mathematics and Statistics, Banasthali University, Banasthali (304022), India.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760952, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {800 - 809}, title = {ANNIHILATOR DOMINATION NUMBER OF TENSOR PRODUCT OF PATH GRAPHS}, key = {cite}, author = {Sharma, K. and Sharma, U.} }