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Domination of undirected graphs — A survey

Part of the Lecture Notes in Mathematics book series (LNM,volume 642)

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References

  1. C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  2. E. J. Cockayne, B. L. Hartnell and S. T. Hedetniemi, An Algorithm for two Disjoint Matchings in a Tree (submitted).

    Google Scholar 

  3. E. J. Cockayne, S. Goodman and S. T. Hedetniemi, A Linear Algorithm for the Domination Number of a Tree, Information Processings Letters 4 (1975), 41–44.

    CrossRef  MATH  Google Scholar 

  4. E. J. Cockayne and S. T. Hedetniemi, Optimal Domination in Graphs, IEEE Trans. on Circuits and Systems, Vol. CAS-22 No. 11 (1975), 855–857.

    CrossRef  MathSciNet  Google Scholar 

  5. E. J. Cockayne and S. T. Hedetniemi, Disjoint Independent Dominating Sets in Graphs, Discrete Math (to appear).

    Google Scholar 

  6. E. J. Cockayne and S. T. Hedetniemi, Towards a theory of Domination in Graphs, Networks (to appear).

    Google Scholar 

  7. E. J. Cockayne and S. T. Hedetniemi, On Group Graphs with Disjoint Cliques (submitted).

    Google Scholar 

  8. E. J. Cockayne and S. T. Hedetniemi, Which Treeds do not have Disjoint Matchings, Utilitas Math (to appear).

    Google Scholar 

  9. E. J. Cockayne and S. T. Hedetniemi, Disjoint Cliques in Regular Graphs of degree seven or eight, J. Comb. Theory (to appear).

    Google Scholar 

  10. E. J. Cockayne and F. D. K. Roberts, Computation of Dominating Partitions (submitted).

    Google Scholar 

  11. F. Harary, Graph Theory, Addison-Wesley, Reading, Mass., 1969.

    Google Scholar 

  12. F. Harary, S. T. Hedetniemi and G. Prins, An Interpolation Theorem for Graphical Homomorphisms, Portugal Math 26 (1967), 454–462.

    MathSciNet  Google Scholar 

  13. B. L. Hartnell, Disjoint Matchings in Unicyclic Graphs, Utilitas Math (to appear).

    Google Scholar 

  14. F. Jaegar and C. Payan, Relations du type Nordhaus-Gaddum pour le Nombre d'absorption d'un graphe simple, C. R. Acad. Sc. Paris, Series A, t. 274, (1972), 728–730.

    Google Scholar 

  15. R. Karp, Reducibility Among combinatorial problems, Complexity of Computer Computations (R. E. Miller and J. W. Thatcher eds.), Plenum Press, New York (1972), 85–104.

    CrossRef  Google Scholar 

  16. C. L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, New York, 1968.

    MATH  Google Scholar 

  17. J. Moon and A. Meir, Relations between packing and covering numbers of a tree, Pacific. J. Math Vol 61 No. 1 (1975), 225–233.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. J. Nieminen, Two bounds for the domination number of a graph, J. Inst. Maths. Applics 14 (1974), 183–187.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. E. A. Nordhaus and J. W. Gaddum, On Complementary Graphs, American Math. Monthly 63 (1956), 175–177.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. O. Ore, Theory of Graphs, American Math. Soc. Colloq. Publ. 38, Providence, R. I., 1962.

    Google Scholar 

  21. P. J. Slater, A constructive characterisation of trees having no k maximum matchings (submitted).

    Google Scholar 

  22. V. G. Vizing, A bound on the External Stability Number of a Graph, Doklady A. N. 164 (1965), 729–731.

    MathSciNet  Google Scholar 

  23. V. G. Vizing, The Cartesian product of graphs, Vyč. Sis., 9, 1963, p 30–43.

    MathSciNet  Google Scholar 

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© 1978 Springer-Verlag Berlin Heidelberg

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Cockayne, E.J. (1978). Domination of undirected graphs — A survey. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070371

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  • DOI: https://doi.org/10.1007/BFb0070371

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  • Print ISBN: 978-3-540-08666-6

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