Abstract
The diet algorithm is introduced for the reduction of square-cell lattice patterns to simpler graphs that contain fewer C 4 ‘cells’. By repeated applications of the algorithm, the lattice pattern is converted into a graph representing the skeletal structure of the pattern. Based on the algorithm, equivalence relations and dissimilarity measures are introduced for lattice patterns, providing tools for shape analysis of planar patterns, such as projections of molecular contour surfaces used in molecular design. This algorithm is applied to a series of examples, illustrating the features of the method.
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References
F.Harary, ‘The cell growth problem and its attempted solutions’, in H.Sachs (ed.), Beitrage zur Graphentheorie, Vol. 49, Teubner, Leipzig (1968).
F.Harary and E.M.Palmer, Graphical Enumeration, Academic Press, New York (1973).
S.Golomb, Polyominoes, 2nd edition, Dover, New York (1996).
F.Harary, Graph Theory, Addison-Wesley, Reading (1969).
G.A.Somorjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, Ithaca, NY (1981).
G.A.Somorjai, ‘Modern concepts in surface science and heterogeneous catalysis’, J. Phys. Chem. 94, 1013 (1990).
C.Soteros and S.G.Whittington, ‘Some properties of lattice animals’, J. Phys. A 21, 2187 (1988).
N.Madras, C.Soteros and S.G.Whittington, ‘Statistical properties of lattice animals’, J. Phys. A 21, 4617 (1988).
F.Harary and P.G.Mezey, ‘Similarity and complexity of the shapes of square-cell configurations’, Theor. Chim. Acta 79, 379 (1991).
F.Harary and P.G.Mezey, ‘Chiral and Achiral Square-Cell Configurations and the Degree of Chirality’, in P.G.Mezey (ed.), New Developments in Molecular Chirality, Kluwer, Dordrecht (1991).
M.Gardner, ‘Mathematical games in which players of ticktacktoe are taught to hunt for bigger game’, Scientific American 240 (April), 18 (1979).
H.J.Fleischner, D.P.Geller and F.Harary, ‘Outerplanar graphs and weak duals’, J. Indian Math. Soc. 38, 215–219 (1974).
F. Harary and P.G. Mezey, ‘Cell-shedding transformations, equivalence relations, and similarity measures for square-cell configurations’, Int. J. Quantum Chem. (in press).
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Harary, F., Mezey, P.G. The diet transform of lattice patterns, equivalence relations, and similarity measures. Mol Eng 6, 415–426 (1996). https://doi.org/10.1007/BF00440413
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DOI: https://doi.org/10.1007/BF00440413