By Mikhail E Elyashberg
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Extra info for Contemporary Computer-Assisted Approaches to Molecular Structure Elucidation
26 Chapter 1 A graph is a multigraph if it has a pair of vertices that can be connected with more than one edge. Such edges are called multiple. An example of a multigraph is displayed below: e a d b c A graph is a labeled graph with n edges if all of its vertices are labeled with integers from 1 to n. The numbers 1, 2,. , un, for example: u4 u5 u1 u2 u3 The degree or valence of vertex v of graph G is a measure of the number of edges incidental to v. In the graph displayed above, the degree of vertices u1, u3, u4, u5 is 2 and the degree of vertex u2 equals 4.
3. The disjunction of Ai and Ak corresponds to the non-excluding ‘‘or’’ and is designated by Ai _ Ak (‘‘Either the Ai or the Ak fragment, or both together, are present in the molecule’’). 4. The Boolean function Ai - wj is called an implication. It corresponds to the expression ‘‘if Ai, then wj’’ (‘‘If the molecule contains the Ai fragment, then the spectral feature wj is observed in a spectrum’’). The following identities of Boolean algebra are valid: a ! b ¼ a _ b ¼ b ! 4) are referred to as de Morgan’s laws.
Both atomic combinations and functional groups are discrete units of structure. We will explain a formal logical model of structural unit analysis that is equally applicable to both NMR and IR spectra. The problem of structural unit spectral analysis can be formulated in symbolic logic language as follows. Assume that an experimental spectrum (NMR, IR or Raman) of an unknown compound is measured and the relationships 20 Chapter 1 between the features observed in the spectrum and the structural elements (for instance, correlation tables) are known.