Skip to main content
SpringerLink
Log in

Majorants and minorants for the classes of graphs with fixed diameter and number of vertices

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

We study majorants (minorants) for the classes of n-vertex diameter d graphs, that is, the extremal graphs on which the sharp upper (lower) bounds are attained for the number of distinct radius i balls for every i ≥ 0. We explicitly describe the minorants for all values of n and d, determine when the class of n-vertex diameter d graphs contains majorants, and describe these extremal graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. A. Evdokimov, “Locally Isometric Embeddings of Graphs and the Metric Prolongation Property,” Sibirsk. Zh. Issled. Oper. Ser.1, 1(1), 5–12 (1994)

    MathSciNet  MATH  Google Scholar 

  2. T. I. Fedoryaeva, “On Variety of Metric Balls in Graphs,” in Proceedings of XIV International Conference “Problems of Theoretical Cybernetics” (Penza, 2005) (Moskov. Gos. Univ., Moscow, 2005), p. 159.

    Google Scholar 

  3. T. I. Fedoryaeva, “Variety of Balls in Metric Spaces of Trees,” Diskret. Anal. Issled.Oper. Ser.1, 12(3), 74–84 (2005).

    MathSciNet  MATH  Google Scholar 

  4. T. I. Fedoryaeva, “Diversity Vectors of Balls and Properties of Their Components,” in Proceedings of the VII International Conference “Discrete Models in the Theory of Control Systems” (Moskov. Gos. Univ., Moscow, 2006), pp. 374–378.

    Google Scholar 

  5. T. I. Fedoryaeva, “Diversity Vectors of Balls in Graphs and Estimates of the Components of the Vectors,” Diskret. Anal. Issled. Oper. Ser.1, 14(2), 47–67 (2007) [J. Appl. Indust. Math. 2 (3), 341–356 (2008)].

    MATH  Google Scholar 

  6. T. I. Fedoryaeva, “ExactUpper Estimates of the Number of Different Balls of Given Radius for the Graphs with the Number of Vertices and Diameter Fixed,” Diskret. Anal. Issled. Oper., 16(6), 74–92 (2009).

    MathSciNet  MATH  Google Scholar 

  7. T. I. Fedoryaeva, “On the Graphs With Given Diameter, Number of Vertices, and Local Diversity of Balls,” Diskret. Anal. Issled. Oper. 17(1), 65–74 (2010) [J. Appl. Indust. Math. 5 (1), 44–50 (2011)].

    MathSciNet  MATH  Google Scholar 

  8. F. Harary, Graph Theory (Addison-Wesley, London, 1969; Mir, Moscow, 1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    T. I. Fedoryaeva

Authors
  1. T. I. Fedoryaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. I. Fedoryaeva.

Additional information

Original Russian Text © T.I. Fedoryaeva, 2013, published in Diskretnyi Analiz i Issledovanie Operatsii, 2013, Vol. 20, No. 1, pp. 58–76.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fedoryaeva, T.I. Majorants and minorants for the classes of graphs with fixed diameter and number of vertices. J. Appl. Ind. Math. 7, 153–165 (2013). https://doi.org/10.1134/S199047891302004X

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S199047891302004X

Keywords

Search

Navigation