Discussiones Mathematicae Graph Theory 28(3) (2008)
453-462
doi: 10.7151/dmgt.1419
Vladimir Samodivkin
Department of Mathematics
University of Architecture Civil Engineering and Geodesy
Hristo Smirnenski 1 Blv., 1046 Sofia, Bulgaria
e-mail: vlsam_fte@uacg.bg
Keywords: bondage number, γ-bad/good vertex.
2000 Mathematics Subject Classification: 05C69.
[1] | D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient Dominating Sets in Graphs, in: R.D. Ringeisen and F.S. Roberts (Eds.), Applications of Discrete Mathematics (SIAM, Philadelphia, PA, 1988) 189-199. |
[2] | D. Bauer, F. Harary, J. Nieminen and C.L. Suffel, Domination alteration sets in graphs, Discrete Math. 47 (1983) 153-161, doi: 10.1016/0012-365X(83)90085-7. |
[3] | R.C. Brigham, P.Z. Chinn and R.D. Dutton, Vertex domination-critical graphs, Networks 18 (1988) 173-179, doi: 10.1002/net.3230180304. |
[4] | J.R. Carrington, F. Harary and T.W. Haynes, Changing and unchanging the domination number of a graph, J. Combin. Math. Combin. Comput. 9 (1991) 57-63. |
[5] | J.E. Dunbar, T.W. Haynes, U. Teschner and L. Volkmann, Bondage, insensitivity and reinforcement, in: T.W. Haynes, S.T. Hedetniemi, P.J. Slater (Eds.), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998) 471-489. |
[6] | J.F. Fink, M.S. Jacobson, L.F. Kinch and J. Roberts, The bondage number of a graph, Discrete Math. 86 (1990) 47-57, doi: 10.1016/0012-365X(90)90348-L. |
[7] | G.H. Fricke, T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi and R.C. Laskar, Excellent trees, Bull. Inst. Comb. Appl. 34 (2002) 27-38. |
[8] | J. Fulman, D. Hanson and G. MacGillivray, Vertex domination-critical graphs, Networks 25 (1995) 41-43, doi: 10.1002/net.3230250203. |
[9] | B.L. Hartnell and D.F. Rall, Bounds on the bondage number of a graph, Discrete Math. 128 (1994) 173-177, doi: 10.1016/0012-365X(94)90111-2. |
[10] | B.L. Hartnell and D.F. Rall, A bound on the size of a graph with given order and bondage number, Discrete Math. 197/198 (1999) 409-413, doi: 10.1016/S0012-365X(99)90093-6. |
[11] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in graphs (Marcel Dekker, Inc., New York, NY, 1998). |
[12] | T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in graphs: Advanced topics (Marcel Dekker, Inc., New York, NY, 1998). |
[13] | Hailong Liu and Liang Sun, The bondage and connectivity of a graph, Discrete Math. 263 (2003) 289-293, doi: 10.1016/S0012-365X(02)00770-7. |
[14] | U. Teschner, A counterexample to a conjecture on the bondage number of a graph, Discrete Math. 122 (1993) 393-395, doi: 10.1016/0012-365X(93)90317-M. |
[15] | U. Teschner, A new upper bound for the bondage number of a graphs with small domination number, Aus. J. Combin. 12 (1995) 27-35. |
[16] | U. Teschner, The bondage number of a graphs G can be much greater than Δ(G), Ars. Combinatoria 43 (1996) 81-87. |
[17] | U. Teschner, New results about the bondage number of a graph, Discrete Math. 171 (1997) 249-259, doi: 10.1016/S0012-365X(96)00007-6. |
[18] | Yue-Li Wang, On the bondage number of a graph, Discrete Math. 159 (1996) 291-294, doi: 10.1016/0012-365X(96)00347-0. |
Received 20 September 2007
Revised 14 July 2008
Accepted 14 July 2008