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.
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References
Bondy, J.A.: A graph reconstructor’s manual. In: Surveys in Combinatorics, (A.D. Keedwell, ed.) London Math. Soc., Lecture Notes, Vol. 166. pp. 221-252,1991
Bondy, J.A., Hemminger, R.L.: Graph reconstruction-a survey, J. Graph Theory1, 227- 268 (1977)
Fiorini, S., Lauri, J.: On the edge reconstruction of graphs which triangulate surfaces, Q. J. Math. Oxf. II. Ser.33, 191–214 (1982)
Lauri, J.: Edge-reconstruction of planar graphs with minimum valency 5, J. Graph Theory3, 269–286 (1979)
Myrvold, W.J., Ellingham, M.N., Hoffman, D.G.: Bidegreed graphs are edge recon- structible, J. Graph Theory11, 281–302 (1987)
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, 1990
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Zhao, Y. On the edge reconstruction of graphs embedded on surfaces. Graphs and Combinatorics 9, 391–395 (1993). https://doi.org/10.1007/BF02988326
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DOI: https://doi.org/10.1007/BF02988326