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2020 | 145 | 234-244
Article title

Strong Efficient Co-Bondage Number of Some Graphs

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Abstracts
EN
Let G = (V, E) be a simple graph. A subset S of V(G) is called a strong (weak) efficient dominating set of G if for every v ∈ V(G), |N_s [v]∩ S|=1. (|N_w [v]∩ S|=1), where N_s (v) = {u ∈V(G) : uv∈ E(G), deg u ≥ deg v}. (N_w (v) = {u ∈V(G) : uv∈ E(G), deg v ≥ deg u}). The minimum cardinality of a strong (weak) efficient dominating set of G is called the strong (weak) efficient domination number of G and is denoted by γ_se(G) (γ_we(G)). A graph G is strong efficient if there exists a strong efficient dominating set of G. The strong efficient co-bondage number 〖bc〗_se(G) is the maximum cardinality of all sets of edges X ⊆ E such that γ_se (G+X) γ_se(G). In this paper, the strong efficient co-bondage number of some standard graphs and some special graphs are determined.
Year
Volume
145
Pages
234-244
Physical description
Contributors
author
  • Department of Mathematics, The M.D.T. Hindu College, Tirunelveli, Tamil Nadu, India
  • Department of Mathematics, The M.D.T. Hindu College, Tirunelveli, Tamil Nadu, India
References
  • [1] M. Anitha and S. Balamurugan, Strong Efficient Open Domination in Graphs. Int. J. Math. And Appl. 6(1–B) (2018) 337-342
  • [2] S. Balamurugan, M. Anitha and N. Anbazhagan, Some Results On Strong Efficient Open Domination. International Journal of Pure and Applied Mathematics Volume 119 No. 15, 2018, 641-648
  • [3] D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient dominating sets in graphs. Application of Discrete Mathematics, 189 – 199, SIAM, Philadephia, 1988.
  • [4] D.W Bange, A.E. Barkauskas, L.H. Host and P.J. Slater, Generalized domination and efficient domination in graphs. Discrete Mathematics, 159, 1-11, 1996.
  • [5] Dorota Kuziak, Iztok Peterin and Ismael G. Yero, Efficient open domination in graph products. DMTCS, 16(1) (2014) 105-120.
  • [6] Frank Harary, Teresa W. Haynes, Peter J. Slater, Efficient and Excess Domination in Graphs. JCMCC 26 , 83-95, 1998
  • [7] H. Gavlas and K.Schultz, Efficient Open Domination. Electron. Notes Discrete Math. 11 (2002), 681-691.
  • [8] J.H. Hattingh, M.A. Henning, On strong domination in graphs. J. Combin. Math. Combin. Compute. 26, 73-82, 1998.
  • [9] V.R. Kulli, Nonbondage number of graphs and diagraphs. International Journal of Advanced Research in Computer Sci and Technology, 3(1), 55-65 (2015)
  • [10] V.R. Kulli and B. Janakiram, The Cobondage Number of a graph. Discussiones Mathematicae, Graph Theory 16 (1996) 111-117
  • [11] V.R. Kulli and B Janakiram, The maximal domination number of a graph, Graph Theory Notes of New York. New York Academy of Sciences, 33, 11-13 (1997).
  • [12] V. R. Kulli and B. Janakiram, The total global domination number of a graph. Indian J. Pure Appl. Math. 27, 537-542 (1996).
  • [13] V.R. Kulli and D.K. Patwari, Total Efficient domination in graphs. IRJPA, 6(1) (2016), 227-232
  • [14] V.R. Kulli and N. D. Soner, Efficient bondage number of a graph. Nat. Acad. Sci. Lett. 19 (9 and 10), 197-202 (1996)
  • [15] N. Meena, A. Subramanian, V. Swaminathan, Strong Efficient Domination and Strong Independent Saturation Number of Graphs. International Journal of Mathematics and Soft Computing, Vol. 3, no. 2, 41-48, 2013
  • [16] N. Meena, A. Subramanian and V. Swaminathan, Strong Efficient Domination in Graphs. International Journal of Innovative Science, Engineering & Technology, Vol. I Issue 4, 172-177, June 2014.
  • [17] K. Murugan, Square Graceful Labeling of Some Graphs. International Journal of Innovative Research in Science, Engineering and Technology, Vol. 4, Issue 2, 511–520 February 2015.
  • [18] Paulraj Joseph J and Arumugam S, Domination and connectivity in graphs. International Journal of Management and Systems, Vol. 8 No. 3, 2330236, 1992.
  • [19] N. Pratap Babu Rao, N. Sweta, Strong Efficient Domination in Jump Graphs. International Journal of Innovative Research in Science, Engineering and Technology, Vol. 7, Issue 4, April 2018, 4011-4014.
  • [20] D. Rautenbach, Bounds on strong domination number. Discrete Math 215 (2000) 201-212.
  • [21] E. Sampathkumar and L. Pushpalatha, Strong weak domination and domination balance in a graph. Discrete Math. 161: 235-242, 1996.
  • [22] A. Senthil Thilak, Sujatha V Shet and S.S. Kamath, Changing and unchanging efficient domination in graphs with respect to edge addition. Mathematics in Engineering, Science and Aerospace Vol. 11, No 1, 201-213, 2020.
  • [23] Teschner, U, New results about the bondage number of a graph. Discret. Math. 171, 249-259, 1997.
  • [24] J.M. Xu, On bondage numbers of graphs a survey with some comments. International Journal of Combinatorics, vol. 2013, Article ID 595210, 34 pages, 2013.
  • [25] Ulrich Teschner, New results about the bondage number of a graph. Discrete Mathematics, Volume 171, 249-259, 1994
Document Type
article
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Identifiers
YADDA identifier
bwmeta1.element.psjd-323bb3b6-68ff-456b-8572-596e5f2ec368
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