Mathematical remarks

Part of the Lecture Notes in Chemistry book series (LNC, volume 42)


The preceding sections dealt with the graphical representations of model spaces, therefore it is quite natural to look for associations with the graph theory on one side, and group-theoretical methods to characterize these model spaces on the other. However, examining books on graph theory (cf Ore 1962; Harary 1969; Deo 1974; Beineke and Wilson 1978; Swamy and Thulasiraman 1981) I have found rather little relevant material. Although it is possible to fit some problems into “structural graph theory” of Nash-Williams (1973) it seems to me that the graph theory is at present not very useful in setting up and analyzing graphs representing model spaces. The graphs used here are real digraphs (directed graphs) in the sense of the theory of graphs but we are really interested in representations of model spaces rather than the graphs themselves. Therefore, although formally the three graphs of Fig 35 are equivalent the first is the most natural, because the contribution of each arc to the total N and M S numbers is clearly visible and we may introduce a horizontal axis to measure N, M S values. In the two other cases we have to label each arc with two weights, one for the number of electrons associated with it (e k = 0,1,2) and one for Ŝz projection numbers (m k = 0, ±1/2).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • W. Duch
    • 1
    • 2
  1. 1.Max-Planck-Institut für Physik und AstrophysikGarching bei MünchenDeutschland
  2. 2.Instytut FizykiUMKToruńPoland

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