Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

CHROMATIC SUMS OF NONSEPARABLE SIMPLE MAPS ON THE PLANE

  • Li, Zhaoxiang (Department of Mathematics, Central University for Nationalities) ;
  • Liu, Yanpei (Institute of Mathematics, Northern Jiaotong University)
  • Published : 2003.05.01

⟨ Previous Next ⟩

Abstract

In this paper we study the chromatic sum functions for rooted nonseparable simple maps on the plane. The chromatic sum function equation for such maps is obtained . The enumerating function equation of such maps is derived by the chromatic sum equation of such maps. From the chromatic sum equation of such maps, the enumerating function equation of rooted nonseparable simple bipartite maps on the plane is also derived.

Keywords

References

  1. Annals of Combinatorics v.5 Dichromatic polynomical and potts models summed over rooted maps R.J. Baxter
  2. J. Combin. Theory v.B40 A survey of asymptotic behaviour of maps E.A.Bender;L.Bruce Richmond
  3. J. Combin. Theory v.A49 The asymptotic number of rooted nonseparale maps on a surface E.A. Bender;N.C.Wormald
  4. Canad. J. math v.15 Enumerotion of non-separable planar maps W.G.Brown
  5. Canad. J. math v.16 on the enumeration of rooted non-separable planar maps W.G.Brown;W.T.Tutte
  6. Physica v.57 On the random-cluster model, I:introduction and relation to other models C.M.Fortuin;P.W.Kasteleyn
  7. J. Combin. Theory Ser. v.B 53 The number of rooted 2-connected triangular maps on the projective plane Z.C.Gao
  8. J.Phys.Soc.Japan, Suppl v.26 Phase transitions in lattice systems with random localproperties P.W.Kasteleyn;C.M.Fortuin
  9. Kluwer, Dordrecht Enumerative Theory of Maps Yanpei Liu
  10. On chromatic and dichromatic sun equations for planar maps v.84 On chromatic and dichromatic sun equations for planar maps Yanpei Liu
  11. Comm.Appl.Math.Comput v.2 Chromatic sum equations for rooted nonseparable planar maps (in Chinese with English Abstract) Yanpei Liu
  12. J.Combin.Theory v.B31 Chromatic polynomials for regular graphs and modified wheels Beatrice Loerinc
  13. Discrete Mathematics v.204 Chromatic polynomials of homeomorphism classes of graphs Ronald C.Read;Earl Glen Whitehead Jr
  14. Canad. J. Math. v.25 Chromatic sums for rooted planar triangulations : the case λ=1 and λ=2 W.T.Tutte
  15. Canad. J. math v.26 Chromatic sums for rooted planar triangulations Ⅳ: the case = λ∞ W.T.Tutte
  16. J.Combin.Theory v.9 On chromatic polynomials and the golden ratio W.T.Tutte
  17. Proceedings of Symposium in Pure Math, Amer.Math.Soc. v.29 Dichromatic sums for rooted planar maps W.T.Tutte
  18. J.Combin.Theory v.B66 Dichromatic sums revisited W.T.Tutte