Abstract
A graphG may have more than one point-baseB G. In a primordial graphP of Rashevsky's (1954) TransformationT, some of the pointbases may consist of nonspecialized points only, and some other pointbases may contains specialized points. In this case, Rashevsky's Theorem (1955a) on point-bases may not hold. The Theorem is certainly true ifall point-bases ofP consists of nonspecialized points. A rigorous proof is given. Some results are derived for the more general case, when point-bases include both kinds of points. A general expression for the point-base ratio of the transformed graphP(T) is obtained. It is shown that with some biologically plausible assumptions Rashevsky's interpretation of the point-base ratio and his conclusions are still true. A few simple Theorems on point-bases of graphs are included in this work.
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Literature
König, Denes. 1936.Theorie der endlichen und unendlichen Graphen. Leipzig: Akademische Verlagsgesellschaft.
Rashevsky, N. 1954. “Topology and Life: In Search of General Mathematical Principles in Biology and Sociology”Bull. Math. Biophysics,16, 317–48.
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Trucco, E. A note on Rashevsky's theorem about point-bases in topological biology. Bulletin of Mathematical Biophysics 18, 65–85 (1956). https://doi.org/10.1007/BF02477844
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DOI: https://doi.org/10.1007/BF02477844