Preferences help
enabled [disable] Abstract
Number of results
2020 | 145 | 342-353
Article title

Concepts Arising from Strong Efficient Domination Number. Part I

Title variants
Languages of publication
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 dominating set 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 bondage number b_se (G) of a non empty graph G is the minimum cardinality among all sets of edges X⊆E such that γ_se (G-X)>γ_se (G). In this paper, the strong efficient bondage number of some path related graphs and some special graphs are studied.
Physical description
  • 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
  • [1] A. Ayta, T. Turacı and Z.N. Odaba. On the Bondage Number of Middle Graphs. Mathematical Notes, 93: 5-6 (2013) 795-801
  • [2] A. Ayta, Z.N. Odaba¸ and T. Turacı. The Bondage Number of Some Graphs. Comptes Rendus de Lacademie Bulgare des Sciences, 64: 7 (2011) 925-930
  • [3] 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
  • [4] D.W Bange, A.E. Barkauskas and P.J. Slater, Efficient dominating sets in graphs, Application of Discrete Mathematics, 189 – 199, SIAM, Philadephia, 1988.
  • [5] 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.
  • [6] K. Ebadi and L. Pushpalatha, Smarandachely Bondage number of a graph. Int. Journal Math. Combin. 4 (2009), 9-19.
  • [7] Frank Harary, Teresa W. Haynes, Peter J. Slater, Efficient and Excess Domination in Graphs. JCMCC 26, 83-95, 1998.
  • [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] J. Ghoshal, R. LaskaR, D. Pillone and C. Wallis, Strong bondage and strong reinforcement numbers of graphs. Congr. Numeran. 108 (1995) 33-42
  • [11] Hartnell, B.L., Douglas F. Rall., Bounds on the bondage number of a graph. Discrete Mathematics, 128 (1994) 173-177
  • [12] Hartnell BJ, Rall DF (1994). Bounds on the bondage number of a graph. Discrete Math. 128, 173-177
  • [13] R. JahirHussain and R. M. KarthikKeyan, 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), pp 10-20
  • [14] John Frederick Fink, Michael S. Jacobson, Lael F. Kinch and John Roberts, THE Bondage Number of a Graph. Discrete Mathematics 86 (1990) 47-57
  • [15] Kang L, Yuan J (2000). Bondage number of planar graphs. Discrete Math. 222: 191-198
  • [16] V.R. Kulli and N. D. Soner, Efficient bondage number of a graph. Nat. Acad. Sci. Lett. 19 (9 and 10), 197-202 (1996)
  • [17] N. Meena, A. Subramanian and V. Swaminathan, Strong Efficient domination in Graphs, International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 4, 172-177, June 2014.
  • [18] N. Meena & D. Uma Parvathy, Strong Efficient Bondage Number of Some Standard Graphs, Enrich, VIII(II), 88- 96, 2017.
  • [19] K. Murugan, Square Graceful Labeling of Some Graphs, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 4, Issue 2, February 2015, 511-520
  • [20] E. Sampathkumar and L. Pushpa Latha. Strong weak domination and domination balance in a graph. Discrete Math. 161: 235-242, 1996.
  • [21] S. Sandhya, C. Jayasekaran and C. David Raj. (2013) Harmonic Mean Labeling of Degree Splitting Graphs. Bulletin of Pure and Applied Science, 32E, 99-112.
  • [22] Teschner U (1995). A new bound for the bondage number of graphs with small domination number. Australas. J. Comb. 12: 27-35
  • [23] U. Teschner. The bondage number of a graphs G can be much greater than ∆(G). Ars. Combinatoria 43 (1996) 81-87
  • [24] U. Teschner, New results about the bondage number of a graph. Discrete Math. 171 (1997) 249-259
  • [25] Yue-Li Wang. On the bondage number of a graph. Discrete Math. 159 (1996) 291-294
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.