Abstract
Let G=(V,E) be a simple graph. A function f:V → { − 1, + 1} is said to be a reverse signed dominating function if the sum of its function values over any closed neighborhood is at most zero. The reverse signed domination number of a graph G equals the maximum weight of a reverse signed dominating function of G. In this paper, we show that the decision problem corresponding to the problem of computing the reverse signed domination number is NP-complete. Furthermore, We present a linear time algorithm for finding a maximal reverse signed dominating function in an arbitrary tree.
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References
Chartrand, G., Lesniak, L.: Graphs and Digraphs, 2nd edn. Wadsworth and Brooks Cole, Monterey (1986)
Barabàsi, A.L., Oltvai, Z.N.: Network biology: understanding the cells functional organization. Nature Reviews Genetics 5, 101–113 (2004)
Dehmer, M., Emmert-Streib, F.: Structural Similarity of Directed Universal Hierarchical Graphs: A Low Computational Complexity Approach. Apllied Mathematics and Coputation 194, 67–74 (2006)
Dunbar, J.E., Hedetniemi, S.T., Henning, M.A., Slater, P.J.: Signed Domination in Graphs. Combinatorics, Graph Theory, Applications 1, 311–322 (1995)
Hattingh, J.H., Henning, M.A., Slater, P.J.: On the Algorithmic Complexity of Signed Domination in Graphs. Australas. J. Combin. 12, 101–112 (1995)
Favaron, O.: Signed Domination in Regular Graphs. Discrete Math. 158, 287–293 (1996)
Lee, C.M.: On the complexity of signed and minus total domination in graphs. Information Processing Letters 109, 1177–1181 (2009)
Gao, M.J., Shan, E.F.: The Signed Total Domination Number of Graphs. ARS Combinatoria 98, 15–24 (2011)
Wang, H.C., Tong, J., Volkmann, L.: A Note on Signed Total 2-independence in Graphs. Utilitas Mathematica 85, 213–223 (2011)
Berliner, A.H., Brualdi, R.A., Deaett, L., Kiernan, K.P., Meyer, S.A., Schroeder, M.W.: Signed Domination of Graphs and (0,1)-Matrices. Combinatorics and Graphs 531, 19–42 (2010)
Atapour, M., Tabriz, S.M.S., Khodkar, A.: Global signed total domination in graphs. Publicaiones Maathematicae-Debrecen 79, 7–22 (2011)
Dewdney, A.K.: Fast Turing Reductions Between Problems in NP 4. Report 71, University of Western Ontario (1981)
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Li, W., Huang, Z., Feng, Z., Xing, H., Fang, Y. (2012). The Algorithmic Complexity of Reverse Signed Domination in Graphs. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34041-3_109
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DOI: https://doi.org/10.1007/978-3-642-34041-3_109
Publisher Name: Springer, Berlin, Heidelberg
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