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- W2088165033 abstract "It is the object of this paper to study the topological properties of finite graphs that can be imbedded in the n-dimensional integral lattice (denoted Nn). The basic notion of deletability of a node is first introduced. A node is deletable with respect to a graph if certain computable conditions are satisfied on its neighborhood. An equivalence relation on graphs called reducibility and denoted by ∼ is then defined in terms of deletability and it is shown that (a) most important topological properties of the graph (homotopy, homology and cohomology groups) are ∼-invariants, (b) for graphs imbedded in N3 different knot types belong to different ∼-equivalence classes, (c) it is decidable whether two graphs are reducible to each other in N2 but this problem is undecidable in Nn for n ≥ 4. Finally, it is shown that two different methods of approximating an n-dimensional closed manifold with boundary by a graph of the type studied here lead to graphs whose corresponding homology groups are isomorphic." @default.
- W2088165033 created "2016-06-24" @default.
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- W2088165033 date "1972-10-01" @default.
- W2088165033 modified "2023-09-25" @default.
- W2088165033 title "SGML results in computational topology" @default.
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- W2088165033 doi "https://doi.org/10.1109/swat.1972.22" @default.
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