# 臺灣博碩士論文加值系統

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 In this thesis, we study the signed domination problem from an algorithmic point of view. In particular, we present some linear algorithms for finding the signed domination numbers of some special block graphs, such as block path and good block graph that every block of G has at least one vertex which is not a cut-vertex of G.
 Abstract........................................................iiContents.......................................................iii1.Introduction....................................................12.Definitions and Notation........................................3 2.1Graphterminology.............................................3 2.2Domination,signed domination and related variation...........4 2.3Block graphs.................................................73.Signed Domination in Block Paths................................84.Signed Domination in Good Block Graph..........................15References......................................................21
 [1] A.V. Aho, J.E. Hopcroft and J.D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, Reading, MA, 1974.[2] I. Broere, J.E. Dunbar and J.H. Hattingh, Minus k-subdomination in graphs. Ars Combin. 50 (1998) 177-186.[3] I. Broere, J.H. Hattingh, M.A. Henning, and A.A. McRae, Majority domination in graphs, Discrete Math. 138 (1995) 125-135.[4]K.S. Booth and J.H. Johnson, Dominating set in chordal graphs, SIAM I. Comput. 11(1982) 191-199.[5] Gerard J. Chang and George L. Nemhauser, R-domination on block graphs, Operation Research Letters, vol. 1, no. 6, (1982) 214-218.[6] Gerard J. Chang, Total domination in block graphs, Operation Research Letters 8 (1989) 53-57.[7] Gerard J. Chang, Sheng-Chyang Liaw and Hong-Gwa Yeh, k-subdomination in graphs, Discrete Applied Math. 120 (2002) 55-60.[8] E.J. Cockayne and C.M. Mynhardt, On a generalization of signed dominating functions of graphs, Ars Combin. 43 (1996) 235-245.[9] J.E. Dunbar, S.T. Hedetniemi, M.A. Henning, and P.J. Slater, Signed domination in graphs, Proceedings of the Seventh International Conference on Graph Theory, Combinatorics, Algorithms and Applications, 1994, pp. 311-321.[10] O. Favaron, Signed domination in regular graphs, Discrete Math. 158 (1996) 287-293.[11] M. Fischermann, Block graphs with unique minimum dominating sets, Discrete Math. 240 (2001) 247-251.[12] M.R. Garey and D.S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-completeness, Freeman, New York(1979).[13] F. Harary, A Characterization of block graphs, Canad. Math. Bull. Vol. 6 no. 1, Jan. 1963.[14] J.H. Hattingh, M.A. Henning and P.J. Slater, On the algorithmic complexity of signed domination in graphs, Australas. J. Combin. 12 (1995) 101-112.[15] J.H. Hattingh, E. Ungerer and M.A. Henning, Partial signed domination in graphs, Ars Combin. 48 (1998) 33-42.[16] M.A. Henning, Domination in regular graphs, Ars Combin. 43 (1996) 263-271.[17] M.A. Henning and P.J. Slater, Inequalities relating domination parameters in cubic graphs, Discrete Math. 158 (1996) 87-98.[18] Le Tu Quoc Hung, Maciej M. Syslo, M.L. Weaver and D.B. West, Bandwidth and density for block graphs, Discrete Math. 189 (1998) 163-176.[19] Li-Ying Kang, Chuangyin Dang, Mao-cheng Cai and Erfang Shan, Upper bounds for the k-subdomination number of graphs, Discrete Math. 247 (2002) 229-234.[20] U.Tesohner, On the bondage number of block graphs, Ars Combin. 46 (1997) 25-32.[21] Hong-Gwa Yeh and Gerard J. Chang, Algorithmic aspects of majority domination, Taiwanese J. Math. Vol. 1, no. 3, 343-350, Sep. 1997.[22] B. Zelinka, Some remarks on domination in cubic graphs, Discrete Math. 158 (1996) 249-255.
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