Abstract
In his thesis [3] B. D. Thatte conjectured that ifG=G 1,G 2,...G n is a sequence of finitely many simple connected graphs (isomorphic graphs may occur in the sequence) with the same number of vertices and edges then their shuffled edge deck uniquely determines the graph sequence (up to a permutation). In this paper we prove that there are such sequences of graphs with the same shuffled edge deck.
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References
F. Harary:Graph Theory. Addison Wesley, New York, 1969.
C. St. J. A. Nash-Williams: The recontruction problem. Chap. 8Selected Topics in Graph Theory. (L. Beineke and R. Wilson, eds) Academic Press, London, 1978.
B. D. Thatte:Reconstruction problems in graph theory. Ph. D. Thesis, Indian Institute of Science, Bangalore, 1990.
B. D. Thatte: On the Nash-Williams' Lemma in graph reconstruction theory.J. Combin. Theory, Ser. B, to appear.
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This research was partially supported by Hungarian National Foundation of Scientific Research Grant no. 1812
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Miklós, D. Disproof of a conjecture in graph reconstruction theory. Combinatorica 12, 367–369 (1992). https://doi.org/10.1007/BF01285825
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DOI: https://doi.org/10.1007/BF01285825