Largest Graphs of Diameter 2 and Maximum Degree 6

  • S. G. Molodtsov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)

Abstract

The results of computer generation of the largest graphs of diameter 2 and maximum degree 6 are presented. The order of such graphs is equal 32. There are exactly 6 graphs of diameter 2 and maximum degree 6 on 32 vertices including one vertex-transitive graph.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dinneen, M.J.: New results for the degree/diameter problem. Networks 24, 359–367 (1994)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    The degree/diameter problem for graphs, http://maite71.upc.es/grup_de_grafs/grafs/taula_delta_d.html
  3. 3.
    Hoffman, A.J., Singleton, R.R.: On Moore graphs with diameters 2 and 3. IBM J. Res. Develop. 4, 497–504 (1960)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Erdös, P., Fajtlowicz, S., Hoffman, A.J.: Maximum degree in graphs of diameter 2. Networks 10, 87–90 (1980)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Elspas, B.: Topological constrains on interconnected-limited logic. In: Proc. 5th Ann Symp. Switching Circuit Theory and Logic Design, pp. 133–147 (1964)Google Scholar
  6. 6.
    Molodtsov, S.G.: Computer-aided generation of molecular graphs. MATCH 30, 213–224 (1994)MATHGoogle Scholar
  7. 7.
    Faradjev, I.A.: Constructive enumeration of combinatorial objects. In: Problemes Combinatoires et Theorie des Graphes, Colloque Internationale CNRS, vol. 260, pp. 131–135 (1978)Google Scholar
  8. 8.
    Cambell, L., Carlsson, G.E., Dinneen, M.J., Faber, V., Fellows, M.R., Langston, M.A., Moore, J.W., Mullhaupt, A.P., Sexton, H.B.: Small diameter symmetric networks from linear groups. IEEE Trans. Comput. 41, 218–220 (1992)CrossRefGoogle Scholar
  9. 9.
    McKay, B.D., Miller, M., Širáň, J.: A note on large graphs of diameter two and given maximum degree. J. Combin. Theory Ser. B 74, 110–118 (1998)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • S. G. Molodtsov

There are no affiliations available

Personalised recommendations