Abstract
A finite To topology, or an acyclic transitive digraph, partitions its underlying point set uniquely into certain ordered subsets called chains, and the size of a chain is the number of points in it. This paper shows that if a To topology, or an acyclic transgraph, satisfies a prescribed condition then, for any. i, the number of chains with size i is set-reconstructible.
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References
J.A. Bondy and R.L. Hemminger, Graph Reconstruction—A survey, J. Graph Theory, 1 (1977).
S.K. Das, A Partition of Finite To Topologies, Canad. J. Math., 25(1973), 1137–1147.
S.K. Das, On the structure of Finite To+T5 Spaees, Canad. J. Math., 25(1973), 1148–1158.
S.K. Das, A Machine Representation of Finite To Topologies. Journal of the ACM., 24(1977), 676–692.
S.K. Das, Some studies in the Theory of Finite Topologies, Doctoral thesis submitted to the University of Calcutta, 1979.
B.D. McKay, Computer Reconstruction of Small Graphs, J. Graph Theory, 1(1977), 281–283.
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© 1981 Springer-Verlag
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Das Kumar, S. (1981). Set-reconstruction of chain sizes in a class of finite topologies. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092266
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DOI: https://doi.org/10.1007/BFb0092266
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11151-1
Online ISBN: 978-3-540-47037-3
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