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2020 | 146 | 22-35
Article title

Concepts Arising from Strong Efficient Domination Number. Part II

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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),degu≥degv}(N_w (v){u∈V(G),uv∈E(G),degv≥degu}. The minimum cardinality of a strong (weak) efficient dominating set of G is called the strong (weak) efficient domination number of G and denoted by γ_se (G)(γ_we (G)). The strong efficient non bondage number b_sen (G) is the maximum cardinality of all sets of edge X⊆E such that γ_se (G-X) = γ_se (G). In this paper, the strong efficient non bondage number of some corona related graphs are studied.
Year
Volume
146
Pages
22-35
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] D.W. Bange, A.E. Barkauskas, L.H. Host, P.J. Slater, Generalized domination and efficient domination in graphs. Discreten Mathematics, 159, 1-11, (1996).
  • [2] D.W Bange, A.E. Barkauskas and P.J. Slater. Efficient dominating sets in graphs. Application of Discrete Mathematics, 189 – 199, SIAM, Philadephia, 1988.
  • [3] E. J. Cockayne and S. Hedetniemi. Towards a theory of Domination in Graphs. Networks, 7(3) (1977) 247-261
  • [4] Deepak. G., Indiramma. M. H., Bindu. M.G. Bondage Number of Lexicographic Product of Two Graphs. International Journal of Innovative Technology and Exploring Engineering Volume 8, Issue 9, 1735-1740, July 2019.
  • [5] Dorota Kuziak, Iztok Peterin, Ismael G. Yero, Efficient open domination in graph products. Discrete Mathematics and Theoretical Computer Science Vol. 16, 1, 105-120, 2014.
  • [6] M. Fischermann, D. Rautenbach, L. Volkmann, Remarks on the bondage number of planar graphs. Discrete Math. 260 (2003) 5767
  • [7] Fink, J.F., Jacobson, M.S., Kinch, L.F., Roberts, J. The bondage number of a graph. Discrete Math. 86 (1990) 47-58
  • [8] H. Gavlas and K. Schultz. Efficient open domination. Electron. Notes Discrete Math. 11: 681-691, 2002.
  • [9] H. Gavlas, K. Schultz, and P. Slater. Efficient open domination in graphs. Sci. Ser. A Math. Sci. 6: 77-84, 2003
  • [10] Hartnell, B.L., Douglas F. Rall. Bounds on the bondage number of a graph, Discrete Mathematics, 128 (1994) 173-177
  • [11] R. Jahir Hussain and R. M. Karthik Keyan. The Kp - Bondage And Kp - Non Bondage Number of Fuzzy Graphs and Graceful Graph. IOSR Journal of Electrical and Electronics Engineering Volume 12, Issue 3 Ver. V (May – June 2017), 10-20
  • [12] R. Jemimal Chrislight, Y. Therese Sunitha Mary The Nonsplit Bondage Number of Graphs, International Journal of Computer Sciences and Engineering, Vol.-7, Special Issue, 5, p74- 76, March 2019,.
  • [13] Kang, L., Yuan, J.: Bondage number of planar graphs. Discret. Math. 222, 191-198, 2000.
  • [14] Krzywkowski. M. 2-Bondage in graphs. Int. J. Comput. Math. 90, 1358-1365, 2013.
  • [15] Liu, H., Sun, L. The bondage and connectivity of a graph. Discret. Math. 263, 289-293, (2003)
  • [16] N. Meena, Strong Efficient Domination Number of Inflated Graphs of Some Standard Graphs. International Journal of Scientific and Innovative Mathematical Research Volume 2, Issue 5, May 2014, 435-440
  • [17] N. Meena, A. Subramanian and V. Swaminathan, Strong Efficient Domination in Graphs. International Journal of Innovative Science, Engineering and Technology, Vol. 1, Issue 4, June 2014.
  • [18] N. Meena, A. Athi Lakshmi, Some Results on Strong efficient non bondage number. Enrich, Vol VIII (I), July – December, 74-82, 2016
  • [19] K. Murugan and N. Meena, Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets. Journal of New Results and Science, Number 11, 04-16, 2016
  • [20] Nagoor Gani and K. Prasanna Devi. Edge Domination and Independence in Fuzzy Graphs. Advances in Fuzzy Sets and Systems, 15(2), 73-84, 2013.
  • [21] Nagoor Gani, K. Prasanna Devi, Muhammad Akram, Bondage and Non-Bondage Number of a Fuzzy Graph. International Journal of Pure and Applied Mathematics Volume 103 No. 2, 215-226, 2015
  • [22] N. Pratap Babu Rao, On Non Bondage Number of a Jump Graph. International Journal of Mathematics Trends and Technology volume 57, Issue 4, 292-295, May 2018.
  • [23] E. Sampathkumar and L. Pushpalatha, Strong weak domination and domination balance ina graph. Discrete Math. 161:235-242, 1996.
  • [24] S. Sandhya, C. Jeyasekaran and C. David Raj, Harmonic Mean Labeling of Degree Splitting graphs. Bulletin of Pure and Applied Science 32E, 99-112, 2013.
  • [25] 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.
  • [26] Teschner, U, New results about the bondage number of a graph. Discret. Math. 171, 249-259, 1997
  • [27] 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.
  • [28] Ulrich Teschner, New results about the bondage number of a graph. Discrete Mathematics, Volume 171, 249-259, 1994.
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bwmeta1.element.psjd-140eb975-a0eb-40fb-9f09-694fffa038ab
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