Chemical graphs. IX. Isotope‐isomerism of multiply‐labelled compounds

Abstract

SUMMARYGeneralizations of previous Jigure-counting series used in Pdlya's enumeration theorem are exploited to enable us to predict the number of isomers of multiply-labelled compounds. Nomenclature problems for such isotope-isomers are reviewed.

Systematic Search for New Types of Chemical Interconversions: Mathematical Models and Some Applications

“…In this section, the main types of generation problems (mentioned in section 1) are shown to be reduced to multistep graph labeling problems, i.e., to sequential distribution of suitable labels between vertices or edges of a given graph. It should be noted that graph labelings are commonly used (see, e.g., ref ) in order to describe generation and enumeration procedures for various derivatives, e.g., heteroanalogs, homologs, or other substitution products of a given organic structure.…”

“…The above formulated labeling problem is evidently very similar to labeling problems for substituted derivatives of a given structure (cf. ref ); the resulting reaction equations were, in fact, considered by several investigators 21 in relation to specific classes of chemical interconversions.…”

“…Although a great variety of enumeration problems is discussed in modern literature, most of them actually relate to orbits of the induced groups Γ‘ = E H . The corresponding enumeration techniques (based mainly on the famous Pólya's Theorem 32a ) make it possible to easily solve counting problems for numerous substituted derivatives of organic structures; the above-cited refs a,b,d,e can serve as typical examples. The very similar “Pólya-like” methods were also used by S. Fujita who has enumerated “reaction graphs” 4b,c and “reaction-center graphs” 21c-e (in other words, symbolic and reaction equations) starting from a given “basic reaction graph”; the last type of graphs uniquely corresponds to “trivial” symbolic equations in which all bonds are formed from zero or completely destroyed.…”

Regioselective deuteration kinetics of 2,3,6‐trimethyl‐4‐phenylpyrylium and 2,6‐dimethyl‐3,4‐diphenylpyrylium salts (1)

“…or a -i s o p r o p y l groups ( 8 ) i n t h i s r e a c t i o n f o r unsymmetrically-substituted pyrylium salts. Recently (9) it was observed t h a t t h e r e i s a marked d i f f e r e n c e i n d e u t e r a t i o n r a t e s between two a-methyl groups ( i n p o s i t i o n s 2 and 6) i f the pyrylium salt i s unsymmet r i c a l l y s u b s t i t u t e d by having a Bubstituent i n p o s i t i o n 3 : t h u s 2,3,4,6-tetramethylpyrylium (1) and 2,4,6-trimethyl-3-phenylpyrylium (2) afforded r e l a -0362-4803/83/09110S-08$1.00 0 1983 by John Wiley & Sons, Ltd. Received May 19, 1983 ii 06 A . T. BaZaban e t a t .…”