The NSM of a Graph

  • Dara Moazzami
Part of the Mathematics and Its Applications book series (MAIA, volume 329)


The purpose of this paper is to introduce a new invariant for measures of stability in networks. Since many network properties are actually properties of the underlying graph, we restrict this discussion to undirected graphs. We prove a number of basic results about this new parameter, including several relating it to other parameters of a graph, operations on graph, and Hamiltonian properties.


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  1. [1]
    M. Behzad, G. Chart rand, and L. Lesniak, Graphs and Digraphs 1979, Prindle, Weber and Schmitt.Google Scholar
  2. [2]
    G. Chartrand, S. F. Kapoor, and D. R. Lick, n-Hamiltonian graphs, J. Combin. Theory 9 (1970), 305–312.MathSciNetGoogle Scholar
  3. [3]
    V. Chvàtal, Tough graphs and Hamiltonian circuits, Discrete Math. 5 (1973), 215–228.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    V. Chvàtal and P. Erdös, A note on Hamiltonian circuits, Discrete Math. 2 (1972), 111–113.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    M. Cozzens, D. Moazzami, and S. Stueckle, The tenacity of a graph, submitted SIAM J. Discrete Math.Google Scholar
  6. [6]
    M. Cozzens, D. Moazzami, and S. Stueckle, Tenacity of the Harary graph, to appear in J. Combin. Math, and Combin. Comput.Google Scholar
  7. [7]
    L. L. Doty, A large class of maximally tough graph, OR Spektrum 13 (1991), 147–151.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    H. Enomoto, B. Jackson, P. Katerinis, and A. Saito, Toughness and the existence of K-factors, J. Graph Theory 9 (1985), 87–95.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    W. D. Goddard and H. C. Swart, On the toughness of a graph, Quaestiones Math. 13 (1990), 217–232.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    D. Mann and S. Stueckle, Tenacity of trees, in preparation.Google Scholar
  11. [11]
    J. C. Molluzzo, Toughness, Hamiltonian connectedness and n-Hamiltonicity, Annals N. Y. Acad. Sci. 319, Proceedings of Second International Conf. on Comb. Math., New York, 1979 (A. Gewirtz, et al., eds.), 402–404.Google Scholar
  12. [12]
    T. Nishizeki, 1-tough nonhamiltonian maximal planar graphs, Discrete Math. 30 (1920, 305–307MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    R. E. Pippert, On the toughness of a graph, in Graph Theory and its Application, Lect. Notes in Math. 303, Springer, Berlin, 1972 (Y. Alavi, ed.), 225–233.Google Scholar
  14. [14]
    Sein Win, On a Connection Between Existence of A-trees and the toughness of a Graph, Graphs and Combinatorics 5, 201–205 (1989).MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    D.R. Woodwall, The binding number of a graph and its Anderson number, J. Combin. Theory Ser. B 15 (1973), 225–255.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Dara Moazzami
    • 1
  1. 1.Center for Theoretical Physics and Mathematics (AEOI)Shahid Beheshti UniversityTehranIran

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