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.
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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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