Advertisement

Graphs and Combinatorics

, Volume 9, Issue 2–4, pp 391–395 | Cite as

On the edge reconstruction of graphs embedded on surfaces

  • Yue Zhao
Graphs and Combinatoric

Abstract

In this paper, we proved that ifG is a 3-connected graph of minimum valency δ = 6χ + 5 with α a non-negative integer and if there exists an embedding ψ ofG on a surface Σ of characteristic ϰ(Σ) = — α|V(G)∣+ β with the representativity of the embedding ψ ≥ 3, where ψ ε 0,1, thenG is edge reconstructible.

Keywords

Planar Graph Regular Graph Open Unit Disc Positive Genus Graph Reconstructor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bondy, J.A.: A graph reconstructor’s manual. In: Surveys in Combinatorics, (A.D. Keedwell, ed.) London Math. Soc., Lecture Notes, Vol. 166. pp. 221-252,1991Google Scholar
  2. 2.
    Bondy, J.A., Hemminger, R.L.: Graph reconstruction-a survey, J. Graph Theory1, 227- 268 (1977)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fiorini, S., Lauri, J.: On the edge reconstruction of graphs which triangulate surfaces, Q. J. Math. Oxf. II. Ser.33, 191–214 (1982)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Lauri, J.: Edge-reconstruction of planar graphs with minimum valency 5, J. Graph Theory3, 269–286 (1979)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Myrvold, W.J., Ellingham, M.N., Hoffman, D.G.: Bidegreed graphs are edge recon- structible, J. Graph Theory11, 281–302 (1987)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Robertson, N., Vitray, R.: Representativity of surface embeddings. In Paths, Flows, and VLSI-Layout (B. Korte, L. Lovász, H.J. Prömel and A. Schrijver, eds), pp. 292–328 Springer Verlag, Berlin, 1990Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Yue Zhao
    • 1
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA

Personalised recommendations